In the present paper, a new characterization of orthogonality monic polynomials sequence $\left\{ Q_{n}\right\} _{n\geq 0}$ is obtained. This defined as linear combination another orthogonal P_{n}\right\} such as% \begin{equation*} Q_{n}(x)+r_{n}Q_{n-1}(x)=P_{n}(x)+s_{n}P_{n-1}(x)+t_{n}P_{n-2}\left( x\right) +v_{n}P_{n-3}\left( +w_{n}P_{n-4}(x),\ n\geq 0 \end{equation*}% where $w_{n}r_{n}\neq 0...