Generalized reciprocity is the phenomenon that individuals treat others in the same way that others treated them in the past. Besides the behavioral outcomes, whether intention information also manipulates generalized reciprocal behavior remains unclear. By conducting two rounds of the dictator game, the current research investigated the influence from the dictator's intention on the receiver's following resource allocation performance. In the games, in order to allocate, either tokens in Experiment 1 or jobs in Experiment 2, a general tendency was shown to treat others better if one was generously treated than greedily treated. Regarding the intentionality, participants who received a generous offer (vs. greedy offer) from another person (i.e., intentional) would perform more generously to another person. However, if the offer was randomly given by a computer program (i.e., unintentional), the way in which one was being treated previously, became somewhat irrelevant to the participants' generalized reciprocal behaviors. Those findings verified the influence of the manipulation of intention on generalized reciprocity, and provided enlightenment for promoting friendly social interactions.