The ac loss of a superconducting cable conductor carrying an ac current is small. Therefore the ratio between the inductive (out-of-phase) and the resistive (in-phase) voltages over the conductor is correspondingly high. In vectorial representations this results in phase angles between the current and the voltage over the cable close to 90 degrees. This has the effect that the loss cannot be derived directly using most commercial lock-in amplifiers due to their limited absolute accuracy. However, by using two lock-in amplifiers and an appropriate correction scheme the high relative accuracy of such lock-in amplifiers can be exploited. In this paper we present the results from ac-loss measurements on a low loss 10 metre long high temperature superconducting cable conductor using such a correction scheme. Measurements were carried out with and without a compensation circuit that could reduce-the inductive voltage. The 1 mu V cm(-1) critical current of the conductor was 3240 A at 77 K. At an rms current of 2 kA (50 Hz) the ac loss was derived to be 0.6 +/- 0.15 W m(-1). This is, to the best of our knowledge, the lowest value of ac loss of a high temperature superconducting cable conductor reported so far at these high currents.