Abstract: Given two sets of functional data having a common underlying mean function but different degrees of distortion in time measurements, we provide a method of estimating the time transformation necessary to align (or 'register') them. The novelty of the method lies in the elimination of prior smoothing, which can be an impediment to good performance. We prove that the proposed method is consistent under fairly general conditions. Simulation results show superiority of the performance of the proposed method over two existing methods. The proposed method is illustrated through the analysis of three paleoclimatic data sets. (This work was done jointly with Dibyendu Bhowmick and Radhendushka Srivastava.)