Credal networks generalize Bayesian networks relaxing numerical parameters. This considerably expands expressivity, but makes belief updating a hard task even on polytrees. Nevertheless, if all the variables are binary, polytree-shaped credal networks can be efficiently updated by the 2U algorithm. In this paper we present a binarization algorithm, that makes it possible to approximate an updating problem in a credal net by a corresponding problem in a credal net over binary variables. The procedure leads to outer bounds for the original problem. The binarized nets are in general multiply connected, but can be updated by the loopy variant of 2U. The quality of the overall approximation is investigated by promising numerical experiments.