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The S transform is a useful linear time-frequency distribution with a progressive resolution. Since it is linear, it filters efficiently in a time-frequency domain by multiplying a mask function. Several different inverse algorithms exist, which may result in different filtering effects. The conventional inverse S transform (IST) proposed by Stockwell is efficient but suffers from time leakage during filtering. The recent algorithm proposed by Schimmel and Gallart has better time localization during filtering but suffers from a reconstruction error and the frequency leakage during filtering. In this paper, two new IST algorithms are proposed that have better time-frequency localization in filtering than the previous two methods.