This paper proposes a novel Skyline query: mutual k-Skyband (MkSB) query. Unlike the traditional k-skyband query methods, MkSB executes the Skyline query from a symmetric perspective, and retrieves all the objects which are among both the dynamic k-Skyband (DkSB) of a specified query object q and the reverse k-Skyband (RkSB) of q. Furthermore, the ranking operation is introduced into MkSB due to its importance in data analysis and decision support. Since MkSB needs to perform DkSB and RkSB of q, it traverses the index multiple times, incurring much redundant I/O overhead. The proposed algorithms reduce multiple traversals to a single one, using the information reuse technology and several effective pruning heuristics that significantly cut down I/O accesses. Meanwhile, it is proved that MkSB based on window query (WMkSB) has the lowest I/O cost. Extensive experiments are conducted on both real and synthetic datasets, and the experimental results show that the proposed algorithms are efficient and outperform their competitors, i.e. the basic algorithm based on BBS (branch and bound Skyline). Especially, WMkSB has the least I/O cost and often reduces more than 95% redundant I/O accesses.