In this paper, we propose an algorithm for mining associating rules based on transaction combination, attribute combination, pattern comparison and comparative pattern mapping (CPM), aiming at the databases with a large number of attributes but a small number of transactions which are common in engineering design. There are four main steps in the CPM algorithm. First, it scans and expands the database and converts it into a Boolean matrix. Second, it compresses the Boolean matrix to construct a transaction combination matrix (TCM) and an attribute combination matrix (ACM) for further calculation. Third, it generates comparative patterns by comparing every transaction with other transactions in the ACM and stores the comparative patterns in a CP-tree. Finally, it obtains all frequent closed itemsets by picking up the frequent nodes of each branch in the last layer of the CP-tree and eliminating false frequent closed nodes, and all frequent itemsets are found by disassembling the frequent closed itemsets. By comparing CPM with Apriori, FP-Growth, nonordfp and FPgrowth*, it is indicated that CPM has a satisfactory performance in mining associating rules from databases with multiple attributes, especially for associating rules with low minimum support degree.