Femtosecond pulses with the interpulse periods that are twice the cavity round-trip time accompanied by two decentered TEM_00 beam spots have been obtained with a self-mode-locked Ti:sapphire laser. By use of two photodiodes to measure the beam spots separately, I found that the pulses occurred at alternate spots on successive round trips. The observation can be explained by the presence of a double-pass cavity mode that reproduces itself after two return transits in an effective confocal resonator along an off-axis path rather than by total mode locking.