The influence of the torsion strain on the coefficients lambda(0) and A of the linear dependence of the magnetostriction constant on the applied stress, lambda = lambda(0) + A sigma, has been investigated in a non-magnetostrictive Co-Fe (Co-rich) amorphous wire. The measurements of the magnetostriction were carried out by means of the small-angle magnetization rotation (SAMR) method on the as-quenched and Joule heated wire. The current annealing was carried out at 550 mA (similar to 450 degrees C) for 2 min. For the as-quenched samples, the magnetostriction is negative and increases with torsion, despite the negative sign of its strain derivative.