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This paper proposes a new minimax method for designing even-order finite-impulse-response (FIR) variable fractional-delay (VFD) digital filters with both the peak errors (maximum absolute errors) of variable frequency response (VFR) and VFD response being minimized. We call such a new minimax design the bi-minimax design, which minimizes a mixed error function that contains both the VFR peak error and VFD peak error. A relative weighting factor is used in the mixed error function for adjusting the relative weightings of the two peak errors. The central part of the biminimax design is how to formulate the biminimax design with highly non-linear constraints on the VFD errors as a solvable one. After linearizing the highly non-linear constraints as linear ones, the biminimax design problem can be easily solved by using the well-known efficient software SeDuMi. As a result, both the VFR peak error and VFD peak error can be simultaneously suppressed and the resulting VFR errors and VFD errors are made nearly equiripple (bi-equiripple). As compared with the existing SOCP-based minimax design that minimizes only the VFR peak error, the proposed biminimax method can achieve a nearly biequiripple design for both the VFR and VFD errors. A design example is given to illustrate the effectiveness of the biminimax design method.