The theoretical treatment for quantum mechanical rotation of polyatomic molecules is performed based on algebra and representations of SO(4) group . Usually the algebra and representations of SU(2) group used in the traditional theory of polyatomic molecular rotation. The properties of molecules in binary rotational state are predicted: 1) disappearrances from a rotational spectrum of polar molecules that lines, which have identical angular momentum number of upper and lower rotational levles, 2) molecules in binary rotational state have an additional energy for the account of quadrupole moment, if the molecule appears in a nonuniform electrical field. The existence of binary rotational states is predicted which have not an analogue in the traditional theory of polyatomic molecular rotation. The connection between binary rotation, classical theory of an asymmetric rotator and traditional theory of molecular rotation is traced.