Princess Cut Diamonds

Short Answer: Yes.

Long Answer: No, because it is simply not worth it for a variety of reasons. For you get a round cut diamond to be turned into a princess cut, you would need to pay a jeweler a large fee, and you would have to decrease the size of your diamond thus decreasing the value.

However, there are techniques of tweaking the round cut diamond rings setting to give it a more square look, like the princess cut.

I feel it is not worth it, if you really want a princess cut that badly, you'll just have to buy it. But if the ring has extreme sentimental value, go talk to a jeweler.