We investigated whether the order of gaze shifts affected spatial and temporal aspects of discrete bimanual pointing movements. Ten male participants concurrently executed bimanual pointing movements as quickly and accurately as possible to left and right lateral targets presented with the same and different amplitudes. They were asked to gaze initially at the left target and subsequently at the right target, or vice versa. Each hand showed less variable error and a faster reaction when the initial gaze shifted to the corresponding target than when the subsequent gaze shifted to it. For the same-amplitude targets, constant error (CE) was not influenced by the gaze order conditions. However, for the different-amplitude targets, CE for the short-amplitude target became larger when they initially gazed at the long-amplitude target than when they initially gazed at the short-amplitude target. The larger overshoot of the hand for the short-amplitude target occurred when the participants could not afford to foveate the target. Our results suggest that the order of gaze shifts determines whether asymmetric amplitude assimilation between the two hands occurs or not. Fast, consistent, and accurate bimanual pointing movements might be attributable to updating gaze-centered representations of target positions.