This paper continues the description of a two parameter family of solutions for the local asymptotic behaviour of UCM fluids at re-entrant corners. Here, the natural stress basis is used to re-derive the equations in the core flow and boundary layers, with full description of the scalings and matching being given. The parametric solution dependence is completed with numerical deteremination of the coefficient of the downstream wall shear rate. The flow structure implicitly assumes the absence of a separating streamline in the upstream region. (C) 2007 Elsevier B.V. All rights reserved.