  A Monte Carlo algorithm for computing quantum mechanical expectation values
of coordinate operators in many body problems is presented. The algorithm, that
relies on the forward walking method, fits naturally in a Green's Function
Monte Carlo calculation, i.e., it does not require side walks or a bilinear
sampling method. Our method evidences stability regions large enough to
accurately sample unbiased pure expectation values. The proposed algorithm
yields accurate results when it is applied to test problems as the hydrogen
atom and the hydrogen molecule. An excellent description of several properties
of a fully many body problem as liquid $^4$He at zero temperature is achieved.
