  We propose a new type of Monte Carlo approach in numerical studies of quantum
systems. Introducing a probability function which determines whether a state in
the vector space survives or not, we can evaluate expectation values of powers
of the Hamiltonian from a small portion of the full vector space. This method
is free from the negative sign problem because it is not based on importance
sampling techniques. In this paper we describe our method and, in order to
examine how effective it is, present numerical results on the 4x4, 6x6 and 8x8
Heisenberg spin one-half model. The results indicate that we can perform useful
evaluations with limited computer resources. An attempt to estimate the lowest
energy eigenvalue is also stated.
