In interplanetary space, the majority of the Alfvénic fluctuations cannot satisfy the Walén relation even though plasma and magnetic field fluctuations are correlated very well. Finding a proper de Hoffman-Teller (HT) wave frame velocity is thus important for characterizing the Alfvénic fluctuations. Recognizing that the Alfvénic fluctuations emanating from different sizes of solar wind streams have their own HT frames, we propose a new scheme called the wave frame with varying velocity (WFVV) method by considering the local averaged HT frame to find a time-varying profile of HT frame velocity. We apply this WFVV method to two Alfvénic events on 2002 October 14 and 17. Unlike the three other schemes discussed in this study, the WFVV method is preferable because it can provide the HT frame variation in more detail, particularly for the large solar wind changes associated with directional discontinuities observed in the October 14 event. For such Alfvénic structures, a time-dependent HT frame derived from the WFVV method, rather than a constant HT frame, produces a better result of the Walén test together with a smaller convection electric field. The difference of estimated HT frame velocities among different schemes was as large as 30 km s-1 for these two events. In addition, we noted that the degree of Alfvénicity tends to decrease with an increasing variance of HT frame velocity, suggesting that a constant HT frame will also give good results for cases of a small variance of HT frame velocity.