Elastic properties of gas hydrate-bearing sediments (GHBS) are important for identifying and quantifying gas hydrate as well as discriminating the effects of free gas on velocity from that due to overpressure. Elastic properties of GHBS sediments can be estimated from elastic inversion using the elastic impedance. The accuracy of elastic inversion can be increased by using the predicted S-wave velocity (Vs) in the parameter k, which is k = (Vs / Vp)2. However, when Vs is less than about 0.6 kilometer per second, the inversion is inaccurate, partly because of the difficulty in accurately predicting low S-wave velocities and partly because of the large error associated with small k values. A new formula that leads to estimates of only the high-frequency part of velocity is proposed by decomposing Vs into low- and high-frequency parts. This new inversion formula is applied to a variety of well logs, and the results demonstrate its effectiveness for all ranges of Vs as long as the deviation of Vs from the low-frequency part of Vs is small. For GHBS, the deviation of Vs from the low-frequency part of Vs can be large for moderate to high gas hydrate saturations. Therefore, the new formula is not effective for elastic inversion for GHBS unless the gas hydrate effect is incorporated into the low-frequency part of Vs. For inversion of GHBS with Vs greater than about 0.6 kilometer per second, the original formulation is preferable.