In the paper Weron (1996, Statist. Probab. Lett. 28, 165-171), I gave a proof to the equality in law of a skewed stable variable and a nonlinear transformation of two independent uniform and exponential variables. The Chambers et al. (1976, J. Amer. Statist. Assoc. 71, 340–344) method of computer generation of a skewed stable random variable is based on this equality. Unfortunately an error crept into my calculations for alpha=1. This note corrects the error.