Let C be a curve of genus at least 2, r and d coprime numbers. The moduli space M_(r, d) of rank r degree d vector bundles on C is smooth and projective. In 1975 P.E. Newstead claimed that M_(r, d) is birational to Jac(C) x Affine space, but there was a mistake in the proof. It was fixed in 1999 by A. King and A. Schofield. I'll explain their argument.