A novel time-series relationship among four consecutive real-valued single-tone sinusoid samples is proposed based on their linear prediction property. In order to achieve unbiased frequency estimates for a real sinusoid in white noise, based on the proposed four-point time-series relationship, a constrained least squares cost function is minimized based on the unit-norm principle. Closed-form expressions for the variance and the asymptotic expression for the variance of the proposed frequency estimator are derived, facilitating a theoretical performance comparison with the existing three-point counterpart, called as the reformed Pisarenko harmonic decomposer (RPHD). The region of performance advantage of the proposed four-point based constrained least squares frequency estimator over the RPHD is also discussed. Computer simulations are conducted to support our theoretical development and to compare the proposed estimator performance with the RPHD as well as the Cramer-Rao lower bound (CRLB).