The author investigates the hydrodynamic instability of a plasma contained by a strongly non-uniform magnetic field 0 in the frequency region eH0/mic < ω < eH0/mec. It is shown that in a plasma with a sufficiently high collision frequency ν a high-frequency tearing mode (encountered earlier in single-fluid hydrodynamics for frequencies ω < eH0/mic) can develop. In particular, a plasma cylinder with a strong longitudinal magnetic field along which a current is flowing may prove unstable with respect to the perturbations under consideration. It is also shown that there is no Suydam instability in the high-frequency region.