In this paper we provide a new approach to the Fundamental Theorem of As-set Pricing. The proof of this result is usually based on Projection (Separation) Theorems and is far more intuitive. Our approach follow the relation between the projection problem an equivalent least squares problem. More precisely, we will use and iterative procedure in order to obtain solutions of a bounded least square problem. This solutions will give, under some conditions, either the state price vector or the arbitrage opportunity of the problem under consideration.