A model for magnetic reconnection in high-conductivity plasma in the solar corona is analyzed in a strong-magnetic-field approximation. The model includes a Syrovatskii current layer and magnetohydrodynamic (MHD) discontinuities attached to the ends of the layer. A two-dimensional analytical solution for the magnetic field is used to compute the distributions of the plasma flow velocity and plasma density in the vicinity of the corresponding current configuration. The properties of jumps in the density and velocity along the attached discontinuities are studied. Based on the character of the variations of the magnetic field and plasma flows at the MHD discontinuities, it is shown that, with the parameter values considered, an MHDdiscontinuity can include regions of trans-Alfvénic, fast, and slowshocks. The results obtained could be useful to explain the presence of “super-hot” (with effective electron temperatures exceeding 10 keV) plasma in solar flares. Other possible applications of the theory of discontinuous flows near regions of magnetic reconnection to analogous non-stationary phenomena in astrophysical plasmas are noted. © 2017, Pleiades Publishing, Ltd.