The Nakagami m-distribution is used to model different fading environments and shown to fit experimental resutls more accurately than other distributions. In this paper, the probability of symbol error for M-ary QAM with square signal constellation in frequency-nonselective shlow Nakagami fading and additive white Gaussian noise is derived. When Nakagami fading index is integer, the derived resutls leads to the closed-form of a finite series.