The possibility that the type of discontinuous flow changes as the conditions gradually (continuously) change is investigated in connection with the problems arising when the results of numerical simulations of magnetic reconnection in plasma are interpreted. The conservation laws at a discontinuity surface in magnetohydrodynamics admit such transitions, but the socalled transition solutions for the boundary conditions that simultaneously satisfy two types of discontinuities should exist in this case. The specific form of such solutions has been found, and a generalized scheme of permitted transitions has been constructed on their basis. An expression for the jump in internal energy at discontinuity is derived. The dependence of the plasma heating efficiency on the type of discontinuity is considered.