Orienting attention to a point in time facilitates processing of an item within rapidly changing surroundings. We used a one-target RSVP task to look for differences in accuracy in reporting a target related to when the target temporally appeared in the sequence. The results show that observers correctly report a target early in the sequence less frequently than later in the sequence. Previous RSVP studies predicted equivalently accurate performances for one target wherever it appeared in the sequence. We named this new phenomenon attentional awakening, which reflects a gradual modulation of temporal attention in a rapid sequence.