  We study the stability problem of a magnetohydrodynamic current sheet with
the presence of a plasma jet. The flow direction is perpendicular to the normal
of the current sheet and we analyze two cases: (1) The flow is along the
anti-parallel component of the magnetic field; (2) The flow is perpendicular to
the anti-parallel component of the magnetic field. A generalized equation set
with the condition of incompressibility is derived and solved as a
boundary-value-problem. For the first case, we show that, the streaming kink
mode is stabilized by the magnetic field at $V_0/B_0 \lesssim 2$, where $V_0$
and $B_0$ are the jet speed and upstream Alfv\'en speed, and it is not affected
by resistivity significantly. The streaming sausage mode is stabilized at
$V_0/B_0 \lesssim 1$, and it can transit to the streaming tearing mode with a
finite resistivity. The streaming tearing mode has larger growth rate than the
pure tearing mode, though the scaling relation between the maximum growth rate
and the Lundquist number remains unchanged. When the jet is perpendicular to
the anti-parallel component of the magnetic field, the most unstable sausage
mode is usually perpendicular (wave vector along the jet) without a guide
field. But with a finite guide field, the most unstable sausage mode can be
oblique, depending on the jet speed and guide field strength.
