A step-like singularity is predicted theoretically for the capacitance-voltage characteristic of a Schottky diode with an isotypic heterojunction and with a narrow-gap region under the metal, but a wide-gap region in the bulk. If the thickness of the narrow-gap layer exceeds the equilibrium thickness of the space charge region under the metal by a factor not exceeding 2, the boundary of the space charge region crosses the heterojunction if a reverse bias is applied. This is the reason for the singularity of the capacitance-voltage characteristic. Such a singularity can be used to determine the energy-band offset (discontinuity) at the heterojunction and the thickness of the narrow-gap layer. The singularity of the current-voltage characteristic is smoothed out when temperature is increased.