A modification of the Jarosch and Curtis (1973) formulation for the calibration pulse inversion is suggested in an effort to improve its accuracy. The modification involves the introduction of the origin time of the pulse (time of the step in the calibration current) as an additional parameter to be solved in the least-squares inversion. This approach is found to be not completely satisfactory in general, but does improve the solution when a large error in origin time (> ±0.5 sec) is introduced in digitizing the pulse. A typical solution, when the origin time of the pulse has to be determined by least-squares, is accurate to within ± 1 sec in the phase response of a system for periods up to 500 sec. A more satisfactory approach is to record the origin time of calibration pulses on seismograms. Only a minor modification of the existing calibration circuit is necessary to provide a simultaneous signal to a time relay and calibration coil through a double pole switch. For pulses, where the origin time is known accurately, the existing techniques give results accurate to within ± 0.3 sec in phase response.