We present a new proof for the fineness of the classical quadratic simplex method for convex quadratic, linear constrained problems. Our proof is based on showing that any instance that is cycling under the quadratic simplex method is degenerate not just in the traditional sense, but also in the sense that the transformed pivot columns in the Karush-Kuhn-Tucker system do not contain any non-zero values for those primal variables in the basis that have a non-zero coefficient in the quadratic objective. Our proof implies that any index selection rules that is finite for the linear programming problem and relies only on the sign structure of the transformed right hand side and objective is also finite for the quadratic simplex method.