Representations of SUq(2) are labeled by a phase playing the role of a Casimir operator. The coproduct SUq(2) is used to form direct product representations which can be reduced to irreducible ones. Direct product of two representations with given phases can be reduced to a representation with any given phase. Coefficients necessary for this procedure are calculated. The calculation can also be performed in the Fourier transformed space which replaces the phase by an integer. (C) 2004 American Institute of Physics.