B-matrix elements for external rotations are conventionally computed by imposing the Casimir-Eckart condition (CEC). However, this results in matrix elements that not only depend on atomic masses but also on the choice of a moving coordinate frame. A new method to directly calculate the B-matrix elements for external rotations, which avoids these problems, is therefore introduced. An underlying symmetry relation is used to reduce the number of required computations. This method is applied to the dynamics equation in nonredundant generalized coordinates, which enhances the efficiency of the B-matrix internal coordinate molecular dynamics formalism.