We consider T of the unit interval [0,1] into itself which is piecewise C^2 and expanding. Using spectral decomposition of the Perron-Frobenius operator we give a proof of the central limit theorem for some process
(1/n)\sum_{i=0}^n foT^n
where f is a function of bounded variation from [0,1] to R. Then we have shown that the speed of convergence in the central limit theorem is of order 1/\sqrt{n}.