The essential problem here is that you are trying to use positive reinforcement to train a negative behavior. Just as you can't train an animal to do something by punishing them, you cannot train a cat to not do something by rewarding them.

The essential problem here is that you are trying to use positive reinforcement to train a negative behavior. Just as you can't train a cat to do something by punishing them, you cannot train a cat to not do something by rewarding them.

If you give your cat a treat every time he jumps on the desk, so it will leave the desk to eat the treat, it will learn that it should jump onto the desk in order to get a treat.

This is probably the easiest way to get the cat to stop jumping on the desk. If the office has a door, close it. If not, install one.

This is, again, probably the easiest way to do this in the short-term. However, your cat may take to hiding in the office, scratching at the door, or otherwise attempting to defeat the physical measures preventing it from entering the office and jumping on the desk. For a long term solution, you may need to train the cat to not jump on the desk.

This may not be easy for someone to whom any negative reinforcement appears unjustified and cruel, and they may be unable to effectively do this. But in the long run, this is probably the most effective way.

If you give your cat a treat every time it jumps on the desk, so it will leave the desk to eat the treat, it will learn that it should jump onto the desk in order to get a treat.

This is probably the easiest way to get the cat to stop jumping on the desk. If the office has a door, close it. If not, install one, and use it. If you do not have a separate office area you can use undistracted, you are cheating your employer, and need to deal with that first.

This is, again, probably the easiest way to do this in the short-term. However, your cat may take to hiding in the office, scratching at the door, or otherwise attempting to defeat the physical measures preventing it from entering the office and jumping on the desk. 

For a long term solution, you may need to actually train the cat to not jump on the desk:

This may not be easy for someone to whom any negative reinforcement appears unjustified and cruel, and they may be unable to effectively do this. But in the long run, this is probably the most effective way. There are a number of arguments against using any negative reinforcement at all with cats, some of which are presented in this article which @Zaralynda kindly pointed out. While in the cases they examine negative reinforcement would indeed be ineffective, used appropriately it can lead to the desired results.

In particular, it is important that you are not punishing the cat for engaging in a behavior for which there is not another alternative. You aren't going to stop eating food just because someone pokes you with a sharp stick every time they see you doing it - you will just hide it from them, or something. Similarly, you can't train a cat to not scratch furniture or climb drapes unless they have a scratching post or tree to scratch instead.

It is also important that this not be done too heavily. In order to effectively use negative reinforcement to train the cat, you can only use it for one behavior at a time. Doing more than one increases the risk that the cat will associate the punishment with the trainer, rather than the behavior, at which point you will no longer be able to train the cat at all.

As a result of our training efforts, my two cats stopped jumping on the counters before the week was over, and have not done it since, even 3 years later, but are otherwise exactly the way they were.

You could try the training technique I used to teach my cats to stay off the kitchen counter:

Every time I (or anyone else in the family) saw the cat sitting, standing, or otherwise being on top of the counter, we were encouraged to take a plastic spray bottle (filled with water, specially for this purpose) and spray the cat with it.

This was very effective; it only took them a day or two to figure out that they are not supposed to jump onto the counter.

The essential problem here is that you are trying to use positive reinforcement to train a negative behavior. Just as you can't train an animal to do something by punishing them, you cannot train a cat to not do something by rewarding them.

How to Train Your Cat to Repeatedly Jump Onto the Desk

If you give positive reinforcement (giving a treat) to train a negative behavior (not jumping on the desk), the cat will instead learn the corresponding positive behavior (jumping onto the desk), not the negative behavior.

If you give your cat a treat every time he jumps on the desk, so it will leave the desk to eat the treat, it will learn that it should jump onto the desk in order to get a treat.

Imagine the following example:

A child's parents do not want the child to play with matches, so every time his parents discover him holding a box of matches, they give him a piece of candy and take the matches away, placing them on a shelf. Of course, the child will continue take the matches off the shelf every time he wants a piece of candy. In fact, he may not even recognize this as wrong - to him, this is just how he signals to his parents that he wants a piece of candy.

This exactly parallels how the cat will react to being rewarded for leaving the desk.

However, a little thought should reveal a better option:

How to Physically Prevent Your Cat From Jumping Onto the Desk

This is probably the easiest way to get the cat to stop jumping on the desk. If the office has a door, close it. If not, install one.

Imagine the following example:

A child's parents do not want the child to play with matches, so every time his parents discover him holding a box of matches, they take the matches away and place them inside a cabinet locked with a child-proof mechanism. Since the child is not physically capable of getting the matches, he will not have them.

This is, again, probably the easiest way to do this in the short-term. However, your cat may take to hiding in the office, scratching at the door, or otherwise attempting to defeat the physical measures preventing it from entering the office and jumping on the desk. For a long term solution, you may need to train the cat to not jump on the desk.

How to Train Your Cat to Not Jump Onto the Desk in the First Place

If you want to train the cat to not do something, you have to use negative reinforcement. One very effective form of negative reinforcement for cats is using a spray bottle filled with water. Each time the cat jumps on the desk, spray it with the bottle.

Imagine the following example:

A child's parents do not want the child to play with matches, so every time his parents discover him holding a box of matches, they give him a spank and take the matches away, placing them on a shelf. While the child may be physically capable of taking the matches, he now has a definite disincentive to do so, and so does not attempt to get them.

This may not be easy for someone to whom any negative reinforcement appears unjustified and cruel, and they may be unable to effectively do this. But in the long run, this is probably the most effective way.