A method for measuring the critical frequencies of the ionospheric layers to accuracies better than 1 kHz is presented. The method depends on the fact that the intensity of the incoherent backscatter plasma line is a function of the electron number density scale height. At the peak or valley of a layer, more electrons are resonant within a specific frequency resolution cell. When fine-frequency measurements are made of the echo from a long radar pulse, the abrupt signal intensity variations as a function of the frequency permit accurate determination of the critical frequencies. Measurements with the Arecibo Observatory 430-MHz radar of the peak densities show that fluctuations of the order of 0.005% can be detected. The integration time must not be longer than a few seconds or frequency smearing caused by ionospheric changes occurs. Comparison of the upshifted and downshifted plasma line frequencies demonstrates the effect of different reception wavelengths on the resonant frequency and also permits determination of the electron drift velocity.