We report on the observation of quantized conductance in split-gate In0.53Ga0.43As/Ga0.77In0.23As/InP point contacts. For the Schottky gates Au/Cr in combination with p-InP was used. As a result our split-gate point contacts show low pinch-off voltages and no measurable leakage current through the gates. Up to five conductance steps were observed at a temperature of 1.4 K. Our approach to fabricate split-gate Schottky contacts can be used for quantum point contacts operating at higher temperatures as well as for superconductive quantum point contacts.