A new approximate method rapidly solving the integral forms of the steady laminar boundary layer equations is presented. This method is based on the specifications of mutual relationships between integral quantities of the boundary layer so that they satisfy the exact solutions at the stagnation point, the flat plate condition and the separation point without any assumptions of boundary layer velocity profiles. A one-dimensional box scheme is used for computations. In view of the results obtained from a wide variety of applications to boundary layer flows which start from either the stagnation point or the fiat plate condition, the present method may be judged sufficient to yield accurate solutions.