Abstract: The aim of this study is to find the exact solution of a quadratic programming problem with linear constraints of an objective quadratic function written in the canonical form. This study describes a new method which is based on splitting the objective function into the sum of two functions, one concave and the other convex; a new feasible constraint set is built by a homographic transform, in such away that the projection of the critical point of the objective function onto this set, produces the exact solution to the problem on hand. Notice that one does not need to transform the quadratic problem into an equivalent linear one as in the numerical methods; the method is purely analytical and avoids the usage of initial solution. The technique is simple and allows us to find the coefficients of the convex function while moving from one summit to another. The proved theorem is valid for any bound, closed and convex domain; it may be applied to a large number of optimization problems. The obtained results are of great importance to solve separable programming cases.