A new motion vector (MV) composition method, which we call temporal bi-directional dominant vector selection (TBDVS), for frame-skipping transcoding of pre-coded video is presented. The TBDVS utilizes a existing relationship, in pre-coded video, between the pixels of a frame and its reference frame(s) via MVs and selects a dominant MV from a set of candidate MVs to minimize prediction errors. It is general enough to handle frame-skipping, including I frame, in an arbitrary manner from a generic I-B-P frame structure video. Experimental results using cascaded pixel-domain transcoder show performance gain over the existing methods in terms of both quality and bit rate. We also propose a refinement method that adaptively adjusts the search range to further improve the performance at marginal cost.