A decoupled finite element method previously reported^{8), 9)} has been revised by introducing the concept of additive viscosity, which had been proposed by Tanoue et al.¹²⁾, in relation to the TME (Transformation of Momentum equation to the Elliptic equation) scheme. This method has been successfully applied to the problem of die swell flow of viscoelastic (single mode Giesekus model) fluids at high Weissenberg numbers. It is found that introduction of the additive viscosity can improve the convergence behavior remarkably and the results with and without the additive viscosity are in precise agreement with each other. The new decoupled finite element method developed here enables us to predict the die swell flow behavior successfully even at Weissenberg numbers (We) over 1000.