In the standard design of the brain-computer interfaces (BCI) based on the P300 component of the event-related potentials (ERP), target and non-target stimuli are presented at fixed positions in a motionless matrix. Can we let this matrix be moving (e.g., if attached to a robot) without loosing the efficiency of BCI? We assessed changes of the positive peak at Pz in the time interval 300-500 ms after the stimulus onset (P300) and the negative peak at the occipital electrodes in the range 140-240 ms (N1), both important for the operation of the P300 BCI, during fixating a target cell of a moving matrix in healthy participants (n=12). N1 amplitude in the difference (target-non-target) waveforms decreased with the velocity, although remained high (M=-4.3, SD=2.1) even at highest velocity (20°/s). In general, the amplitudes and latencies of these ERP components were remarkably stable in studied types of matrix movement and all velocities of horizontal movement (5, 10 and 20°/s) comparing to matrix in fixed position. These data suggest that, for the users controlling their gaze, the P300 BCI design can be extended to modifications requiring stimuli matrix motion.