Another way to generate a random permutation

Generate n random numbers U1, ..., Un, order them, and then use the indices of the successive values as the random permutation. For instance, if n =5, and U1 = 0.8, U2 = 0.5, U3 = 0.4, U4 = 0.7, U5 = 0.1; then, because U5 < U3 < U2 < U4 < U1, the random permutation is 5, 3, 2, 4, 1. The difficulty of this algorithm is that sorting the random numbers typically requires on the order of nlog(n) computations.