It is shown that the shear flow present in the magnetopause current layer can destabilize the tearing modes depending upon the Mach number profiles. Using a variational principle, an heuristic stability criterion based on the form of the Mach number profile is obtained. This criterion could be used as a handy tool to search for tearing mode instability of a given magnetopause equilibrium with shear flow. The Doppler shifted magnetic structures produced by the tearing modes would be observable at ultralow frequencies in the range of ~5--650 mHz in the satellite frame of reference. ¿ American Geophysical Union 1995