This article presents a new algorithm to solve the coordinate transformation problem of molecular geometry optimization. The algorithm is very fast and its CPU time consumption scales linearly with the system size. It makes use of the locality of internal coordinates by efficient sparse matrix techniques. The new algorithm drastically reduces the time needed for coordinate transformations as demonstrated by test calculations on polyalanine and carbone nanotube systems: for a 2000 atom system it requires just seven seconds, instead of the hours consumed by traditional schemes.