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We introduce an accurate theoretical approach for computing the symbol-error rate (SER) of an M-ary quadrature amplitude modulation (M-QAM) orthogonal frequency division-multiplexing (OFDM) system in the Nyquist rate Cartesian clipping channel. The Cartesian clipper clips the high peak values of the Nyquist rate in-phase/quadrature (I/Q) components of the complex baseband OFDM signal separately. In contrast to previous works that approximate the nonlinear noise, in the frequency domain, as a Gaussian additive random process, an accurate expression is derived for the probability density function (pdf) of the clipping noise at the output of the OFDM demodulator on each subcarrier. The inverse Fourier transform of the characteristic function of the noise is used to derive this accurate pdf. Using this pdf, we can evaluate the performance of the OFDM system for each subcarrier with high accuracy, especially at high backoffs where the Gaussian approximation of the nonlinear noise is no longer valid. The proposed method has the accuracy and validity of the simulation while being comparatively much less time consuming.