Beginning from the bi-variational expression for the standard coupled cluster doubles (CCD) energy, we propose including a term quadratic in the left operator, (S) over cap (dagger)(2). As this makes the left-hand and right-hand wave functions more similar, the resulting functional should better approximate the variational expression. The energy given by the quadratic functional is extensive and the stationary equations may be solved in O(N-6) time. These equations have been implemented and the potential energy surfaces for HF dissociation, H2O double dissociation and NZ dissociation are examined. It is found that the quadratic functional effectively reproduces the fully variational results in all cases.