Let g be the function which maps conformally a simply-connected domain G onto a rectangle R so that four specified points z1, z2, z3, z4,o n ∂G are mapped respectively onto the four vertices

of R. This paper is concerned with the study of a domain decomposition method for computing approximations to g and to an associated domain functional in cases where: (i) G is bounded by two

parallel straight lines and two Jordan arcs. (ii) The four points z1, z2, z3, z4, are the corners where the two straight lines meet the two arcs.