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In classical single-layer fuzzy systems (FSs), the number of rules and the run-time computational requirements increase exponentially with the number of input domains. In this paper, we present a method for converting a multidimensional FS to a two-layer hierarchical FS that reduces the number of rules and improves the run-time efficiency. The first layer of the two-layer system consists of FSs whose rule bases can be represented as linearly independent vectors. The second layer constructs linear combinations of the rule base vectors. The effectiveness of the hierarchical conversion in reducing the number of rules and improving efficiency is demonstrated on a classic control problem and a simulated higher dimensional FS.