Let (X, Y) be a pair of random variables such that X ranges over [0, 1] and Y is real-valued and let go(X) be the conditional expectation of Y given X. Based on a training sample, the piecewise polynomial estimator of go is obtained via usual M-estimates. It is proved that under certain regularity conditions the piecewise polynomial M-estimator achieves the optimal global rate of convergence of estimators for nonparametric regression.