Let be a graph. A set is a restrained dominating set if every vertex not in is adjacent to a vertex in and to a vertex in . The restrained domination number of , denoted by , is the smallest cardinality of a restrained dominating set of . We define the restrained bondage number of a nonempty graph to be the minimum cardinality among all sets of edges for which . Sharp bounds are obtained for , and exact values are determined for several classes of graphs. Also, we show that the decision problem for is NP-complete even for bipartite graphs.