  An exact, nonlocal, finite step-size algorithm for Monte Carlo simulation of
theories with dynamical fermions is proposed. The algorithm is based on
obtaining the new configuration U' from the old one U by solving the equation $
M(U') \eta = \omega M(U) \eta$, where $M$ is fermionic operator, $\eta$ is
random Gaussian vector, and $\omega$ is random real number close to unity. This
algorithm can be used for the acceleration of current simulations in theories
with Grassmann variables. A first test was done for SU(3) QCD with purely
fermionic term in the action.
