A　frame　can　be　completed　to　a　tight　frame　by　adding　some　additional　vectors.　However,　for　the　purpose　of　computational　efficiency,　we　need　to　put　restrictions　to　the　number　of　added　vectors.　In　this　paper　we　propose　a　constructive　method　that　allows　to　extend　a　given　frame　to　an　oblique　dual　frame　pair　such　that　the　number　of　added　vectors　is　in　general　much　smaller　than　the　number　of　added　vectors　used　to　extend　it　to　a　tight　frame.　We　also　present　a　uniqueness　characterization　and　several　equivalent　characterizations　for　an　oblique　dual　frame　pair,　it　turns　out　that　oblique　dual　frame　pair　provides　more　flexibilities　than　alternate　dual　frame　pair.　©　2013　World　Scientific　Publishing　Company.