A method is developed for treating successive rotations in terms of non-linear rotational vector products. Combinations of ordinary vector and scalar products give the same results that can be most commonly achieved by the use of quaternals or 2x2 unit matrices. The method automatically provides the direction of the axis and the value of the unique (single) rotation angle, which is equivalent to the product of two or more successive rotations. This information is not readily and immediately obtained by the usual method of rotation matrices to solve the problem of successive rotations. The method applies to the case of a rotation around the direction {111}, successive π rotations around orthogonal axes, and the treatment of continuous rotations. In addition, it simplifies the problem of calculating crystalline symmetry, where the knowledge of this is of great utility, to predict eigenvalues of the Hamiltonian and, consequently, to predict the number of energetic levels of crystalline systems, by mere considerations of symmetry. The successive rotations allow to verify the (conservation) invariance of symmetry of the system, as well as the Hamiltonian invariance of the system.
