There is an intensive debate on whether memory for serial order is symmetric. The objective of this study was to explore whether associative asymmetry is modulated by memory task (recognition vs. cued recall). Participants were asked to memorize word triples (Experiments 1-2) or pairs (Experiments 3-6) during the study phase. They then recalled the word by a cue during a cued recall task (Experiments 1-4) and judged whether the presented 2 words were in the same or in a different order compared with the study phase during a recognition task (Experiments 1-6). To control for perceptual matching between the study and test phase, participants were presented with vertical test pairs when they made directional judgment in Experiment 5. In Experiment 6, participants also made associative recognition judgments for word pairs presented at the same or the reversed position. The results showed that forward associations were recalled at similar levels as backward associations and that the correlations between forward and backward associations were high in the cued recall tasks. On the other hand, the direction of forward associations was recognized more accurately (and more quickly) than backward associations, and their correlations were comparable to the control condition in the recognition tasks. This forward advantage was also obtained for the associative recognition task. Diminishing positional information did not change the pattern of associative asymmetry. These results suggest that associative asymmetry is modulated by cued recall and recognition manipulations and that direction as a constituent part of a memory trace can facilitate associative memory.