We have previously developed a method for saddle point optimization of densely connected systems (such as metals and their oxides in condensed phase) in Cartesian coordinates. Our method was shown to converge in less than half the number of steps as compared to the next best performing code on one of the optbench.org saddle point optimization benchmarks. This method was implemented in Sella, an open source Python software package we have developed that has bindings to more than 20 popular electronic structure theory software packages due to its integration with the ASE software package. However, Cartesian coordinates and the related algorithms are not efficient for saddle point searches on the potential energy landscapes of sparsely connected atomic systems, such as molecules, because of the strong coupling between atomic degrees of freedom. Molecular optimization (both for minima and saddle points) is generally performed in a basis of internal coordinates, which typically comprise bond stretch distances, bending angles, and dihedral angles, as internal coordinates are significantly less energetically correlated than Cartesian coordinates. These chemically relevant features provide a more effective coordinate system for optimization at the cost of additional algorithmic complexity. We have recently developed a new method for realizing displacements in a basis of redundant internal coordinates which dramatically reduces the number of steps required to reach convergence on a minimization benchmark. In this work, we extend this algorithm to optimization of saddle point geometries.