In the solar wind Alfvénic fluctuations are coupled fluctuations in the transverse components of plasma velocity, , and magnetic field, , in which remains nearly constant. Consequently, the fluctuations in the component of and along the direction of the underlying magnetic field, , are always one-sided relative to base values rather than mean values. This paper proposes a new method for estimating and verifies it using simulation data. The new approach is to find a consistent minimum variance direction of magnetic field for two different data subsets divided by a threshold angle from the original data set. Simulation results show that (1) the direction of predicted by the new method is generally more accurate than the average magnetic field, , and that (2) does not correspond to when the averages of the transverse field fluctuations are nonzero. Two events of one-sided Alfvénic fluctuations in the solar wind observed at 0.36 and 1 au, where a small but significant mean appears in the transverse field fluctuation, are demonstrated for the new method. Results show that the new estimate is more radial than and also different from that predicted by Parker's model of the heliospheric magnetic field (HMF). This new technique will be useful for comparing solar wind observations with the global HMF model and for determining the fluctuation k-vector, which is presumably directed along .