We investigated the influence of magnetostriction on the damping constant (α) of 50-nm-thick NixFe1-x polycrystalline films, with x ranging from 0.66 to 0.86. In the experiments, α and the saturation magnetostriction (λs) were evaluated with high accuracy, which allowed for an interesting finding suggesting a simple relation between and λs. In the range of positive λs, α slightly increases as x decreases, whereas increases from 0.009 to 0.012 with increasing x for negative λs values. reaches a minimum when λs is around zero at x=0.78. These results demonstrate that different behaviors of depend on positive or negative values of λs. Therefore, particular attention should be paid to the change in magnetoelastic properties and the deterioration of magnetic softness when adjusting of magnetically soft films.