One problem that is frequently encountered when constructing internal coordinate systems is bending angles may become nearly or completely linear. This is a problem because linear bending angles do not have a well-defined Cartesian derivative, and dihedral angle coordinates which contain a linear angle are undefined. This problem is typically solved by manually replacing the pathological angle with one or more new coordinates, usually an improper dihedral or in-and out-of-plane bending angles. However, if the central atom of the pathological angle is only bonded to two other atoms, then it is not possible to define a chemically meaningful improper dihedral to replace the angle. In that case, it is necessary to define a new, so-called "dummy" atom, which is used to help define the improper dihedral. For this scenario, we have developed an algorithm for automatically adding dummy atoms to a molecule, potentially even mid-optimization. This is a key aspect of our method, as without automatic reconstruction of internal coordinates, some molecular saddle point optimizations will fail due to the coordinate system becoming ill-defined. To the best of our knowledge, no other optimizer automatically reconstructs the internal coordinate system mid-optimization when the initially constructed internal coordinate system becomes ill-defined.