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Most commercial database management systems sort tuples of a relation by their primary keys for the purpose of supporting efficient insertions, deletions, and updates. However, primary keys are usually auto-generated integers, which bear little useful information about user data. Secondary indexes have to be created sometimes to help retrieve tuples by columns other than the primary key. Evidently, a better solution is to sort the data by columns that appear frequently in retrieval conditions. Unfortunately, this method does not work, at least not immediately, when the relation is vertically partitioned, which is a popular technique to reduce I/O overhead, since it is difficult to keep tuples of two partitions in exactly the same order unless the sorting columns are replicated, which again wastes storage space and disk bandwidth unnecessarily. In this paper, we introduce a positional access method that allows a partition to be sorted by another one but incurs little storage overhead and provide details about how to improve its performance.