  The fermion sign problem, the biggest obstacle in quantum Monte Carlo
calculations, is completely solved in this paper. Here, we find a strategy, in
which the contribution from those negative-weighted paths is thoroughly
cancelled or replaced by some positive-weighted paths. The crucial point lies
on the Feynman path integral formula proposed in our group, which allows us to
deeply analyze the Boltzmann weight of each path. Through mathematical proof,
we demonstrate that physical quantities can be exactly calculated within a
specific kind of paths, which have positive the Boltzmann weight. With this
finding, a new Monte Carlo method is proposed, in which the fermion sign
problem is absent. As an example, the current method is applied to the
two-dimensional Hubbard model, and the results do manifest the correctness.
