Minimum aberration has been studied quite extensively for regular designs since its introduction by Fries and Hunter (1980). Deng and Tang (1999) introduced the generalized minimum aberration (GMA) criterion for selecting both regular and nonregular designs. Using the GMA criterion based on its confounding frequency vector (CVF), Deng and Tang (2002) classified and then ranked various designs taken from Hadamard matrices of orders 12, 16, and 20. However, GMA/CFV cannot separate some non-isomorphic designs when their CVF's are the same. In this paper, we propose a new measure, moment aberration projection (MAP), to classify and rank fractional factorial designs. While CFV measures the relationship among the design columns, MAP measures the relationship among the design rows. We will show that MAP has a much better classification power than CFV. In particular, MAP gives a complete classification for 16-run and 2-level designs with any number of columns. Our empirical evaluations show that MAP ranking are very consistent, but not identical, with the ranking of CFV. Finally, we show another key advantage of MAP over CFV in its applicability to designs with more than 2 levels.