A new method of lasing of single picosecond pulses in a short-cavity dye laser with spatial separation of the lasing medium and the saturable absorber in the case of pumping by nanosecond pulses with energies much higher than the oscillation threshold has been developed and experimentally realized. The method is based on the use of a high-Q, external cavity tuned to the amplification wavelength of the saturable absorber. The first picosecond pulse is lased at a lasing-medium wavelength and the subsequent pulses are lased at a saturable-absorber amplification wavelength.