It is conjectured that the non-linear sigma-model without Wess-Zumino terms is equivalent as a quantum theory to the non-abelian massless Thirring model. However, the standard (Sugawara) current algebra of the non-linear model is not isomorphic to that of the fermionic theory. A new current algebra formalism is proposed, which depends on a parameter k. As k→∞ it reduces to the Sugawara formalism. The new current algebra is isomorphic to the fermionic one, being the direct sum of two Ka-Moody algebras with opposite central terms. In the quantum theory, k(which is the level number) has to be an integer. The new formalism is shown to preserve Poincaré and conformal invariance classically. The new current algebra is derived canonically and a new action principle for the non-linear model is proposed.