  We give an explicit construction of the factorizing twists for the Yangian
Y(sl_2) in evaluation representations (not necessarily finite-dimensional). The
result is a universal expression for the factorizing twist that holds in all
these representations. The method is general enough to recover the universal
R-matrix of Y(sl_2) up to its character in the form specialized to generic
evaluation representations. The method presented here is particularly amenable
to generalizations because it involves only elementary operations applied to
representations of the Yangian.
