We exhibit an explicit pseudorandom generator that stretches an Ow4logw+log(1)logn -bit random seed to n pseudorandom bits that cannot be distinguished from truly random bits by a permutation branching program of width w with probability more than . This improves on the seed length O(w!)11+log(1)logn of Koucky, Nimbhorkar, and Pudlak and Ow8+log(1)logn of De. More importantly, the analysis of our generator uses only combinatorial and linear-algebraic arguments, whereas the previous proofs refer to groups or representation theory.