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In this letter, we develop an optimum transform domain split vector quantization (TrSVQ) method. We address both the issues of achieving best rate-distortion (R/D) performance and less complexity. For quantizing a multivariate Gaussian source, we derive the mean-square error (MSE) performance expression for the TrSVQ method using high rate theory and optimum bit allocation. Also, to reduce the complexity, we develop a binary split- based iterative algorithm and use the algorithm in a tree structured manner to find the optimum subvectors' dimensions (i.e., optimum splits).