Directional discontinuities (DDs) are common structures in the interplanetary space. Correctly determining the normal of a DD is important to understand the changes of phase fronts of magnetic fields adjacent to a discontinuity as well as helpful for the applications in many regimes of space physics research. In this work, we propose a new scheme to estimate the normal directions of DDs by finding the smallest standard deviation of normal magnetic fields derived from the cross product of magnetic fields on both sides of the discontinuity, based on the idea that the phase fronts of the adjacent magnetic fields are closely parallel to the DD plane. By comparing with the normal direction determined from Cluster multiple spacecraft, we show that our scheme can provide the same accuracy as that from the multispacecraft estimation. Moreover, our scheme gives a consistent result of normal estimations at different Cluster spacecraft. We notice that in some cases, the normal directions derived from the minimum variance analysis have large differences between those of multispacecraft method and our scheme implying significant influence of the kinetic effect of particles in the transition region of the discontinuity. A few events of STEREO B observations are further studied to show that our scheme can be applied to DDs in single-spacecraft measurements with even small rotation of magnetic fields across the discontinuities. With the help of an accurate normal estimation, we can understand the variations of magnetic field phase fronts in the vicinity of discontinuities.