  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 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 world-sheet 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.
