By introducing expedient transformations and a set of Lojcjanski parameters [3] into the initial system of differential equations of a laminar plane stationary boundary layer, a universal equation was obtained. Its solution, namely, calculated by numerical integration on an electronic computer and arranged in tables, can be easily used when solving any special case of incompressible fluid flow. The supplementary integration of the impulse equation of the boundary layer, necessary when applying the original method of Lojcjanski [3], becomes redundant in this case, which significantly simplifies the use of this procedure in engineering practice. From the consideration of the obstruction flow of a cylinder of circular cross-section, it follows that already in the one-parameter approximation values close to the correct ones are achieved. At the same time, in comparison with the corresponding one-parameter solution of Lojcjanski, a certain improvement of the obtained results can be observed. Ivanović [2] also came to this conclusion when considering the flow of cylinders of ellipse section for different ratios of its semi-axes. The solution of the same universal equation in the two-parameter approximation obtained by Mirgo [4], further improved the results. This confirmed the satisfactory speed of convergence, which is provided by the procedure developed in this paper. It should also be noted that it has already been successfully extended to more complex physical models of the boundary layer. Namely, on compressible fluid flows (Saljnikov and Boričić [10]), flows of non-Newtonian fluids (Saljnikov and Ćukić [11]) and magnetohydrodynamic flows (Saljnikov and Boričić [12]).