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A comprehensive method to synthesize negative group delay (NGD) in the microwave regime with a maximally flat response is proposed in this paper. This method is based on transversal-filter topologies; it will be shown that by choosing proper coupling coefficients of each tap of a transversal filter, we can realize NGDs with maximally flat characteristics at the output of the transversal filter. The desired coefficients to realize maximally flat NGDs with various amount of group delay are analytically derived and tabulated in this paper. Furthermore, the results are verified experimentally through microwave transversal-filter approaches in both passive and active ways using multi-section asymmetric directional couplers and distributed amplifiers.