A new secant-method based numerical procedure (T-secant method) with super-quadratic convergence (convergence rate 2.618) has been developed for least-squares solving of simultaneous multi-variable nonlinear equations. The basic idea of the procedure is that the original secant equations are modified by a non-uniform scaling transformation “T”, an additional new estimate is determined in each iteration and a completely new set of trial solutions is constructed for the next iteration. The suggested method seems to eliminate the unstable behavior of the traditional method and the efficiency is an order higher than Broyden’s methods in case of the numerical example. The vector-based interpretation and its geometrical representation helps to explain the basic operations. The performance of the new method is demonstrated by the results of numerical tests with a Rosenbrock-type test-function with up to 1000 unknown variables.