Abstract: A linear parabolized stability equations（PSE） for two-dimensional/axisymmetric compressible boundary layers is derived.The linear PSE is discretized in both the streamwise and wall normal directions.The discretization in the streamwise direction is the implicit backward first order and,the wall normal direction,fourth order central finite-difference schemes.The program is validated by the stability problem of Mach 4.5 boundary flows of plate and curvous plates.The instability of blunt body boundary layers is discussed.A new mechanism of instability is found.