Summary: In [Bull. Belg. Math. Soc. - Simon Stevin 17, No. 4, 641–659 (2010; Zbl 1225.42016)] the authors proved that a quasi-symmetric orthogonal polynomial sequence \(\{R_{n}\}_{n \geq 0}\) is a Laguerre-Hahn sequence if and only if the component \(\{P_{n}\}_{n \geq 0}\) in its quadratic decomposition is also a Laguerre-Hahn sequence. In this paper and under these conditions, we deduce the class s of the Laguerre-Hahn sequence \(\{R_{n}\}_{n \geq 0}\). More precisely, if \(s'\) is the class of \(\{P_{n}\}_{n \geq 0}\) then \(2s' \leq s \leq 2s' + 3\). On the other hand the polynomial coefficients of the Riccati equation satisfied by the Stieltjes function corresponding to \(\{R_{n}\}_{n \geq 0}\) are given in terms of those of \(\{P_{n}\}_{n \geq 0}\). As an application, we determine all non-symmetric quasi-symmetric Laguerre-Hahn sequences of class one.