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A new signal subspace approach for sinusoidal parameter estimation of multiple tones is proposed in this paper. Our main ideas are to arrange the observed data into a matrix without reuse of elements and exploit the principal singular vectors of this matrix for parameter estimation. Comparing with the conventional subspace methods which employ Hankel-style matrices with redundant entries, the proposed approach is more computationally efficient. Computer simulations are also included to compare the proposed methodology with the weighted least squares and ESPRIT approaches in terms of estimation accuracy and computational complexity.