Transformations for the stabilization of variance of the binomial and negative binomial distributions are considered. In each case a new transformation is suggested. These transformations are two-term inverse sine and inverse-hyperbolic sine transformations involving six adjustable constants, thus generalizing previous work of Anscombe [1] and of Freeman and Tukey [3]. In the sequel some properties of these transformations are derived. The nature of the dependence of the variances of these transformations on some parameter is worked out and depicted graphically.