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In recent work a solution of the Ornstein-Zernike equation for a general Yukawa closure for a single component fluid was found. Because of the complexity of the equations a simplifying assumption was made, namely that the main scaling matrix Gamma had to be diagonal. While in principle this is mathematically correct, it is not physical because it will violate symmetry conditions when different Yukawas are assigned to different components. In this work we show that by using the symmetry conditions the off diagonal elements of Gamma can be computed explicitly for the case of two Yukawas solving a quadratic equation: There are two branches of the solution of this equation, and the physical one has the correct behavior at zero density. The non-physical branch corresponds to the solution of the diagonal approximation. Although the solution is different from the diagonal case, the excess entropy is formally the same as in the diagonal case.