Abstract: In the paper a new method for solving discontinuous problems——QRCM is proposed.The main difference between QRCM and RCM^[2] is that QRCM transforms the governing equation system (∂u)/(∂t)+A(u)(∂u)/(∂x)=H(u) (A) into mutually independent scalar equations utilizing quasi characterized method^[5] ωi(u)·du|_{(dx)/(dt)=λi}=ωi(u)·H(u)dt ωi(u)·((∂u)/(∂t)+λ₁(∂u)/(∂x)=ωi(u)·H(u) or ωi(u)·du|_{(dx)/(dt)=λi}=ωi(u)·H(u)dt (B) so that solving Riemann problems of (A) can be replaced by solving Rie-mann problem of each (B)'s scalar equation, where λi and ωi(u) are the eigenvalues and eigenvectors respectively of Jacobian mafrix A(u).The method keeps the main advantages of RCM.Especially, it is suitable for parallel computation.Finally,two test examples are computed,the numerical results are sati-sfctory compared with known results.