We present a new geodesic-based method for geometry optimization in a basis of redundant internal coordinates.This method realizes displacements along internal coordinates by following the geodesic generated by the displacement vector on the internal coordinate manifold.Compared to the traditional Newton method approach to taking displacements in internal coordinates, this geodesic approach substantially reduces the number of steps required to reach convergence on a molecular structure minimization benchmark.This new geodesic method can in principle be implemented in any existing optimization code, and only requires the implementation of derivatives of the Wilson B-matrix and the ability to solve a relatively inexpensive ordinary differential equation.