We consider the symmetric Darlington synthesis of a p × p rational symmetric Schur function S with the constraint that the extension is of size 2p × 2p and we investigate what happens when we impose that S and its extension have real coefficients. In this case, under the assumption that S is strictly contractive in at least one point of the imaginary axis, we determine an upper bound for the McMillan degree of the extension. A constructive characterization of all such extensions is provided in terms of a symmetric realization of S and of the outer spectral factor of I− SS*.