This paper presents a second-order projection method for solving the time-dependent, incompressible Navier-Stokes equations. The method is based on a diffusion-convection step followed by a projection step, with enhanced coupling between these steps to achieve second-order accuracy in time. The diffusion-convection step uses a specialized higher-order Godunov method to handle nonlinear convective terms robustly, even at high Reynolds numbers. The projection step is approximated using a Galerkin procedure with a local basis for divergence-free vector fields. Numerical results validate the method's convergence properties and demonstrate its performance on more challenging applications, such as doubly periodic shear layers. The method is shown to be second-order accurate in both space and time, provided the time step is appropriately chosen.This paper presents a second-order projection method for solving the time-dependent, incompressible Navier-Stokes equations. The method is based on a diffusion-convection step followed by a projection step, with enhanced coupling between these steps to achieve second-order accuracy in time. The diffusion-convection step uses a specialized higher-order Godunov method to handle nonlinear convective terms robustly, even at high Reynolds numbers. The projection step is approximated using a Galerkin procedure with a local basis for divergence-free vector fields. Numerical results validate the method's convergence properties and demonstrate its performance on more challenging applications, such as doubly periodic shear layers. The method is shown to be second-order accurate in both space and time, provided the time step is appropriately chosen.