Continuous monitoring of k Nearest Neighbor (kNN) queries has attracted significant research attention in the past few years. A safe region is an area such that as long as a kNN query remains in it, the set of its k nearest neighbors does not change. Hence, the server does not need to update the query results unless the query moves out of its safe region. Previous work uses Time-Parameterized kNN (TPkNN) queries to construct the safe region. In this paper, the authors present an efficient technique to construct safe regions by using much cheaper RangeNN queries.