This paper proposes a simple method to derive a closed-form expression for the exact symbol error probability of Non-Rectangular 22k+1 Amplitude Modulated Phase Modulated (AMPM) signals over an Additive White Gaussian Noise (AWGN) channel. The obtained expression is verified using MATLAB-based computer simulations of AMPM systems for different QAM modulation orders, including QAM8, QAM32, and QAM128. Finally, the derived equation for the exact symbol error probability is compared with the upper-bounded symbol error probability expression for different QAM orders.