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Two-dimensional plasma flows are investigated in the approximation of strong magnetic field for the case of stationary reconnection in a thin current layer with four attached MHD disconti- nuities. The specific features of this approximation are illustrated by the numerical solution of a problem about two-dimensional flows near a thin Syrovatskii reconnecting current layer. The method allows to solve a system of ordinary differential equations instead of partial differential equations system. Two-dimensional velocity field v(x,y,t), the magnetic field B(x,y,t) and the density distribution ρ(x,y,t) are calculated. The method used is applicable for the investigation of the generalized model of a reconnecting current layer with attached MHD discontinuities. The global structure of magnetic field in the vicinity of reconnection region is taken from the analytical solution by Bezrodnykh et al. Astronomy Letters*, 37, 113, 2011.