Wilson fermions with imaginary chemical potential

We study the phase structure of imaginary chemical potential. We calculate the Polyakov loop using clover-improved Wilson action and renormalization improved gauge action. We obtain a two-state signals indicating the first order phase transition for $\beta = 1.9, \mu_I = 0.2618, \kappa=0.1388$ on $8^3\times 4$ lattice volume We also present a result of the matrix reduction formula for the Wilson fermion.