This short paper proposes an alternative rule for choosing the step size in the line search associated with unconstrained nonlinear minimization of \(f(x)\), \(x\in \mathbb{R}^ n\). Given a descent direction \(d_ i\), the usual line search phase is: find \(\alpha_ i\geq 0\) satisfying \(f(x_ i,\alpha_ id_ i)=min\{f(x_ i+\alpha d_ i), \alpha\geq 0\}\). In general, an inexact search has to be performed. The author's alternative line search introduces a parameter \(\beta_ j\), from which \(\gamma_ j=f(x_ i+\beta_ jd_ i)-f(x_ i)-\beta_ jd_ i^ Tg_ i\) is computed \((g_ i=\nabla f(x_ i))\) as part of the modified search procedure. It is proved that the resultant sequence \(\{f(x_ i)\}\) is decreasing and that, if \(f(x)\) is strictly convex quadratic, the alternative line search is exact.