This paper addresses the problem of efficient maintenance of a materialized skyline view in response to skyline removals. While there has been significant progress on skyline query computation, an equally important but largely unanswered issue is on the incremental maintenance for skyline deletions. Previous work suggested the use of the so called exclusive dominance region (EDR) to achieve optimal I/O performance for deletion maintenance. However, the shape of an EDR becomes extremely complex in higher dimensions, and algorithms for its computation have not been developed. We derive a systematic way to decompose a d-dimensional EDR into a collection of hyper-rectangles. We show that the number of such hyper-rectangles is O(md ), where m is the current skyline result size. We then propose a novel algorithm DeltaSky which determines whether an intermediate R-tree MBR intersects with the EDR without explicitly calculating the EDR itself. This reduces the worse case complexity of the EDR...