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This paper proposes a novel method for the design of a recursive second-order (biquadratic) all-pass phase compensator with controllable stability margin. The design idea stems from the generalized stability triangle (GST) derived by the author for the second-order biquadratic digital filter. Based on the GST, a parameter-transformation method is proposed on the transformations of the denominator coefficients of the transfer function of the biquadratic phase compensator. The transformations convert the original denominator coefficients to other new parameters, and any values of those new parameters can guarantee that the GST condition is always satisfied. Optimizing the new parameters yields a biquadratic phase compensator that definitely meets a prespecified stability margin. That is, a biquadratic all-pass phase compensator can be designed to have an arbitrarily specified stability margin. This in turn avoids the occurrence that a recursive phase compensator may become unstable in the practical applications. Thus, the resulting biquadratic phase compensator has robust stability, which is extremely important during the practical filtering operations. A design example is given to show the stability margin guarantee as well as the approximation accuracy. [ABSTRACT FROM AUTHOR]