The properties of equivalent orbitals, as defined in previous parts, are examined in more detail. It is shown that the character of an equivalent set can be deduced knowing the symmetry group of a single orbital of the set. This theorem has several useful applications. Further properties of equivalent sets are found by considering the structure of the molecular symmetry group in relation to the symmetry group of an orbital. An investigation whether or not equivalent orbitals in a molecule are uniquely defined shows that there are still degrees of freedom available which can be used to satisfy additional conditions.