The truncating Fourier and continue wavelet representation of a discontinuous piecewise smooth signal will introduce an unneglectable error which was named as the Gibbs phenomenon. In this paper

we proposed an effective piecewise smooth signal approximation method. Firstly

a set of normal orthogonal piecewise polynomials was constructed according to the given positions of breaking points

and it has the properties of orthogonality

convergence and reproduction. Then the signal was orthogonal decomposed under this basis and the best square approximation result could be obtained using reconstruction. The numerical experiments show that our method have the higher accuracy approximation results than the other basis.