A new mechanism for the formation of pinching plasma instability related to
a tangential discontinuity is discussed. With this in mind we use a simple
model of the Davydov-Zakharov class. It appears that there is a strong dep
endence of the instability increment on current density resulting from the
corresponding dispersion relation. Modulation of a current pulse is shown t
o be a possible way of stabilizing powerful discharges.