- The spectrum of quenched Yang–Mills theory in the large-N limit displays strings and higher-dimensional extended objects. The effective dynamics of string-like excitations is encoded into an area-preserving Schild action. In this letter, we bridge the gap between SU(N) gauge models and fully reparametrization-invariant Nambu–Goto string models by introducing an extra matrix degree of freedom in the Yang–Mills action. In the large-N limit this matrix variable becomes the worldsheet auxiliary field allowing a smooth transition between the Schild and Nambu–Goto strings. The new improved matrix model we propose here, can be extended to p-branes provided we enlarge the dimensionality of the target spacetime.