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In this paper, an important aspect of problems in symbolic image database retrieval (SIDR) is addressed. The problems in conventional pairwise spatial relationships, particularly the 9DLT-matrix-based approach, used to represent a symbolic image in SID are discussed. A new concept called triangular spatial relationship (TSR) is introduced as an improved, invariant spatial relationship to take care of object transformations. A set of quadruples is used to preserve the TSR among the components in a symbolic image. The proposed method is based on principal component analysis. The first principal component vector (PCV) of the set of quadruples is used to represent a symbolic image in SID. The proposed algorithm requires O(logn) search time in the worst case in the recognition phase, where n is the number of symbolic images stored in the symbolic image database.