Self-pumped phase conjugate pulses due to picosecond and femtosecond pulses in near IR have been demonstrated. We generated the conjugate pulses with a BaTiO3 crystal, the direction of the c axis of which in the setup is different from that of the Cat conjugator. The conjugate character of the conjugate pulses are examined with the distorter method. The reflectivity of the picosecond conjugate waves was about six times higher than that of the femtosecond pulses and the rise time of the former was about 30 times faster that of the latter, when the average power of two trains of pulses are equal. Explanation of the phenomenon is proposed.