The problem of frequently updating multi-dimensional indexes arises in many location-dependent applications. While the R-tree and its variants are one of the dominant choices for indexing multi-dimensional objects, the R-tree exhibits inferior performance in the presence of frequent updates. In this paper, we present an R-tree variant, termed the RUM-tree (stands for R-tree with Update Memo) that minimizes the cost of object updates. The RUM-tree processes updates in a memo-based approach that avoids disk accesses for purging old entries during an update process. Therefore, the cost of an update operation in the RUM-tree reduces to the cost of only an insert operation. The removal of old object entries is carried out by a garbage cleaner inside the RUM-tree. In this paper, we present the details of the RUM-tree and study its properties. Theoretical analysis and experimental evaluation demonstrate that the RUMtree outperforms other R-tree variants by up to a factor of eight in scenarios with frequent updates.