By introducing into the Loitsyansky-Bogdanova method [7] the expedient variables of Salnikov-Kukicheva [9], a complete universalization of the equations of a Lemirna incompressible boundary layer in the case of a swirling motion of an axisymmetric body of arbitrary shape has been achieved. The resulting system of equations is numerically solved in the two-parametric once localized approximation. The integration results are presented graphically and analyzed. A method for the practical application of the obtained universal functions by means of these nomograms is shown.