Fractional factorial designs are widely used in practice and typically chosen according to the minimum aberration criterion. A sequential algorithm is developed for constructing efficient fractional factorial designs. A construction procedure is proposed that only allows a design to be constructed from its minimum aberration projection in the sequential build-up process.To efficiently identify nonisomorphic designs, designs are divided into different categories according to their moment projection patterns. A fast isomorphism check procedure is developed by matching the factors using their delete-one-factor projections. A method is proposed for constructing minimum aberration designs using only a partial catalog of some good designs.