That's still a quicksort - it always has n^2 as its worst case I thought? If you pick the wrong pivot each time.
Some others have posted methods (random pivot, median of 3). The gnu libc qsort implementation is a good learning tool (it uses median of 3). I think CLRS has the guaranteed n log n version.
Pick median of three random elements as pivot; it's hard to pick wrong pivot every time unless your RNG always returns 7.
On the other hand, if you are sorting unsanitised input, then random is good, but it should be secure pseudo-random numbers if it's important to your security/performance whilst under attack.