This paper presents a new technique to improve the delay fault coverage by re-ordering flip-flops in a scan chain. Unlike prior techniques where scan flip-flops can be reordered arbitrarily to form a new scan chain order, we restrict the distance by which a scan flip-flop can be moved to create the new scan chain order. The distance restriction makes it practical to make post-synthesis, local layout modifications to accommodate the new scan chain order. It also minimizes the routing overhead required for the new scan chain order. Given a post-synthesis scan chain order, we re-order flip-flops to minimize the number of undetectable faults due to test pattern dependency. Although the distance restriction limits the number of possible new scan chain orders, the fault coverage achieved by using our new local scan chain re-ordering method is comparable or even higher than prior methods. Moreover the scan order obtained with our method also improves the coverage of stuck-open faults. Experimental results show that the proposed method can improve delay fault coverage by up to 21.8% for ISCAS 89 circuits.