The stability of an MHD tangential discontinuity is studied in an inco
mpressible plasma where viscosity is taken into account at one side of
the discontinuity. When the shear velocity is smaller than the thresh
old value for the onset of the Kelvin-Helmholtz (KH) instability, two
surface waves can propagate along: the discontinuity. There is a criti
cal value for the shear velocity, which is smaller than the threshold
value for the onset of the KH instability. When the shear velocity is
smaller than the critical value, the two surface waves propagate in op
posite directions. When the shear velocity is larger than the critical
velocity, the two waves propagate in the same direction, and the wave
with smaller phase velocity is a negative-energy wave. Viscosity caus
es this negative-energy wave to be unstable, and the instability incre
ment is proportional to the viscosity coefficient.