We propose a new multiple imputation technique for imputing squares. Current methods yield either unbiased regression estimates or preserve data relations. No method, however, seems to deliver both, which limits researchers in the implementation of regression analysis in the presence of missing data. Besides, current methods only work under a missing completely at random (MCAR) mechanism. Our method for imputing squares uses a polynomial combination. The proposed method yields both unbiased regression estimates, while preserving the quadratic relations in the data for both missing at random and MCAR mechanisms.