  We derive the recurrence relation of irreducible tensor operator for O(4) in
using the Wigner-Eckart theorem. The physical process like radiative
transitions in atomic physics, nuclear transitions between excited nuclear
states can be described by the matrix element of an irreducible tensor, which
is expressible in terms of a sum of products of two factors, one is a
symmetry-related geometric factor, the Clebsch-Gordan coefficients, and the
other is a physical factor, the reduced matrix elements. The specific
properties of the states enter the physical factor only. It is precisely this
fact that makes the Wigner-Eckart theorem invaluable in physics. Often time one
is interested in ratio of two transition matrix element where it is sufficient
to regard only the Clebsch-Gordan coefficients. In this paper we first get the
commutation relations of O(4), and then we choose one of these relations to
operate on the certain eigenvectors. Finally we take summation over all
possible eigenvectors and obtain rather the compact recurrence relation for
irreducible tensor operators.
