  The Kelvin--Helmholtz (KH) and tearing instabilities are likely to be
important for the process of fast magnetic reconnection that is believed to
explain the observed explosive energy release in solar flares. Theoretical
studies of the instabilities, however, typically invoke simplified initial
magnetic and velocity fields that are not solutions of the governing
magnetohydrodynamic (MHD) equations. In the present study, the stability of a
reconnecting current sheet is examined using a class of exact global MHD
solutions for steady state incompressible magnetic reconnection, discovered by
Craig & Henton. Numerical simulation indicates that the outflow solutions where
the current sheet is formed by strong shearing flows are subject to the KH
instability. The inflow solutions where the current sheet is formed by a fast
and weakly sheared inflow are shown to be tearing unstable. Although the
observed instability of the solutions can be interpreted qualitatively by
applying standard linear results for the KH and tearing instabilities, the
magnetic field and plasma flow, specified by the Craig--Henton solution, lead
to the stabilization of the current sheet in some cases. The sensitivity of the
instability growth rate to the global geometry of magnetic reconnection may
help in solving the trigger problem in solar flare research.
