According to the presently available generally accepted method, the time of minimum of a solar cycle is determined by the minimum of average monthly values of sunspot number which are smoothed for 13 months. Thus, the time of the minimum of a solar cycle is determined with a long delay, not earlier than eight months after the minimum. To resolve this major common problem, we propose a new optimal method for determination of the time of minimum of a solar cycle. Our method allows one to determine the time of minimum of a solar cycle within four months after the minimum. In the new method, the time of minimal average monthly values of the total solar irradiance (TSI) is used as an indicator of the time of minimum of a solar cycle when four subsequent values of the TSI are greater than the preceding minimum value. The TSI data show a better defined minimum than the more "noisy" sunspot data. Here we deduce that the ended 23rd solar cycle minimum took place in July and the new cycle started in August 2008.