Singular R-matrices and Drinfeld's comultiplication

We compute the R-matrix which intertwines two dimensional evaluation representations with Drinfeld comultiplication for U_q(\widehat{sl}_2). This R-matrix contains terms proportional to the delta-function. We construct the algebra A(R) generated by the elements of the matrices L^\pm(z) with relations determined by R. In the category of highest weight representations, there is a Hopf algebra isomorphism between A(R) and an extension \overline{U}_q(\widehat{sl}_2)} of Drinfeld's algebra.