This paper presents an on-wafer calibration algorithm, with fixed probe position constraint, for scattering parameter (S-parameter) measurements without impedance-standard substrate (ISS). The fixed probe position feature is suitable for production tests of radio-frequency integrated circuits (RFICs), where the probe positions designed for the dimension of the device-under-test (DUT) are applied to the associated calibration standards as well, and the probes need not to be moved in X-Y directions during calibrations and measurements. Three on-chip standards are adapted including a transmission line (TL), a series resistor with offset line segment, and a shunt resistor with offset line segment, where the characteristics of the on-chip standards are solved using the self-calibration technique. To show the robustness of the proposed calibration algorithm, simulation studies with noise effects are conducted. Further experimental results are shown with verifications of an independent multiline thru-reflect-line (TRL) calibration data.