The smoothed minimal level of the total solar irradiance is proposed as a new physically justified criterion for the determination of the time of minimum between solar cycles during the sunspot activity minimum. The minimal level of the total solar irradiance values averaged through a month and smoothed for 13 months when the last four of the values exceed the preceding value at the point of minimum shows the time of minimum between the cycles. The new criterion was successfully used for the determination of the time of the preceding minima between the cycles 21 and 22, 22 and 23, as well as 23 and 24.