A longitudinal stability is considered for the quasi-steady current sheet which is uniform along the current. In the MHD approximation, the stability problem is solved for the plane neutral sheet and small disturbances propagating along the current. The current sheet is shown to break-up into the system of cooler and more dense filaments due to radiative cooling. The filaments are parallel to magnetic field lines. This process corresponds to the condensation mode of a thermal instability and can play a trigger role for a solar flare. Moreover, at the nonlinear stage of development, it can lead to the formation of very dense cold filaments surrounded by high-temperature low-density plasma inside the current sheet. Flowing into the filaments, hot plasma is cooled by radiation and compressed. Then the cold dense plasma flows out from the current sheet along the filaments. We think that the process under consideration is responsible for the often observed picture of an arcade of cold loops in the solar corona.