Very wideband TEM-mode transmission-line quadrature hybrids having a small phase ripple and optimum Chebyshev coupling can be realised by compensating the phase characteristics of optimum Chebyshev asymmetric 3dB couplers by means of allpass networks. Numerical results are given in detailed tabular form which enable hybrids with bandwidths up to at least 12:1 to be designed readily without resorting to tandem connections of two looser couplers. Experimental results for a decade-band hybrid show good agreement with the theory.