You don't have to stick with square tapered. But whatever you go to has to match your crankset.
The key measurements are basically the width of your BB shell (yours is 68mm) and the length of the spindle. You can measure your existing spindle, but you may need a different length if you change crank sets. Spindle length is mostly determined by the crank, though occasionally you have to make adjustments depending on frame design.
Think a little about what you want to achieve by "upgrading". It can help performance a lot in some cases. But you can also spend a lot of money upgrading BB and cranks without achieving much of anything.
Why do you want to replace your UN52? Unless the bearings are rough and gravely, you are not going to have any improvement.
On my PDG, I thought that there was a BB issue - I took it out, inspected it, and put it back in; it turned out that it was not properly torqued..... It was the original 1992 vintage UN70. On a bike that had spent a lot of time out side.
Nigel