We show that if v is a symmetric regular Laguerre‐Hahn linear form (functional), then the linear form u defined by u = −λx−2v + δ0 is also regular and symmetric Laguerre‐Hahn linear form for every complex λ except for a discrete set of numbers depending on v. We explicitly give the coefficients of the second‐order recurrence relation, the structure relation of the orthogonal sequence associated with u, and the class of the linear form u knowing that of v. Finally, we apply the above results to the symmetric associated form of the first order for the classical polynomials.