A numerical study of the fluid flow and heat transfer characteristics of the two-dimensional impingement jet with a confinement plate has been carried out. The fluid flow was calculated by solving the full Navier-Stokes equation. In doing that, the well known SIMPLER algorithm was used and the trouble making convection term was discretized according to QUICKER scheme. The energy equation was simply solved by using the SOR method. For the Reynolds number of 10000, two channel heights, say 1.5 and 3.0 times the jet exit width, and two thermal boundary conditions constant wall temperature and constant wall heat flux were considered. Discrete heat sources were flush mounted along the impingement plate at a distance of 0, 2, 3, 4, 5, 6, 10, 12, times the jet exit width from the stagnation point. The length of each heat source is 4 times the jet exit width long. The Nusselt number averaged over each heat source was compared with experiment. Comparison shows that both calculations and experiment have the secondary peak of Nusselt number at downstream of stagnation point, even though there is a little quantitative difference in between. The difference is believed due to abscure thermal boundary condition in experiment and also accuracy of turbulence model used. The secondary peak is shown to be caused by rigorous turbulent flow motion generated as the wall jet flow is retarded and developes into the channel flow without flow reversal.