A new signal subspace approach for estimating the frequency of a single complex tone in additive white noise is proposed in this correspondence. Our main ideas are to use a matrix without repeated elements to represent the observed signal and exploit the principal singular vectors of this matrix for frequency estimation. It is proved that for small error conditions, the frequency estimate is approximately unbiased and its variance is equal to Cramér-Rao lower bound. Computer simulations are included to compare the proposed approach with the generalized weighted linear predictor, periodogram, and phase-based maximum likelihood estimators in terms of estimation accuracy, computational complexity, and threshold performance.