  We test the finite density algorithm in the canonical ensemble which combines
the HMC update with the accept/reject step according to the ratio of the
fermion number projected determinant to the unprojected one as a way of
avoiding the determinant fluctuation problem. We report our preliminary results
on the Polyakov loop in different baryon number sectors which exhibit
deconfinement transitions on small lattices. The largest density we obtain
around $T_c$ is an order of magnitude larger than that of nuclear matter. From
the conserved vector current, we calculate the quark number and verify that the
mixing of different baryon sectors is small.
