An efficient numerical method for computing three-dimensional, unsteady, incompressible flows is presented. To eliminate the restriction of CFL condition, fully-implicit time advancement which the Crank-Nicolson method is used for both the diffusion and convection terms, is adopted. Based on an approximate block LU decomposition method, the velocity-pressure decoupling is achieved. The additional decoupling of the intermediate velocity components in the convection term is made for the fully-implicit time advancement scheme. Since the iterative procedures for the momentum equations are not required, the decouplings of the velocity components lead to the reduction of computational cost. Numerical validations are made for the decaying vortices and the flow inside a square cavity. The present decoupling method is applied to the direct numerical simulation (DNS) of minimal channel flow unit.