The superconducting transition temperatures of copper sulfide CuS are measured as a function of hydrostatic pressure up to about 9 katm by an ice bomb technique. The superconducting transition is detected with the ac Hartshorn mutual inductance bridge. In contrast to ordinary superconductors the curve of the shift of the transition temperature with increasing pressure decrease nonlinearly with downward curvature over the whole range of applied pressures and its slope changes discontinuously at about 3.5 katm. The maximum peak of the imaginary part of the ac susceptibility vanishes under pressurs above about 1.6 katm. It is discussed that the observed unusual behaviour of the transition temperature is probably attributed to a change of the Fermi surface of the type proposed by Lifshitz
