By taking a special constraint for a general realization of Y(sl(2)), two sets of sl(2) algebras are presented, in which a u(1) algebra is hidden. With the help of this constraint, the block-diagonal form can be written to the generator J of Yangian algebras, and especially it is a rotational transformation of a spin in the elementary quantum mechanics. This sheds new light on the physical meaning of Y(sl(2)).