The MUSCL developed by Van Leer is aimed to eliminate or diminish the overshoot usually unavoidable for second ovder shock capturing schemes.It gives narrow transition zone for discontinuities. We tested this scheme by the Riemann problem and by a more complicated problem baring known highly accurate result. Both boundary condition and high temperature singularity should be treated properly. Some knowledge about the adjectable constant used in the monotone algorithm have been accumulated. Besides, a main formula in Van Leer's paper is corrected, the stability condition is refined.