An instanton-like solution is considered for a class of two-dimensional conformal model with Liouville term. The model expressed here is a new higher-dimensional model with scalar-spinor interaction on evendimensional spaces, and is a generalization of the even-dimensional Fujii model. A recurrence relation for the Fujii model and coupling constant's indices between relations with interaction constant is extracted. The behavior of Gürsey, Akdeniz-Smailagić and Fujii coupling constants in 4-dimensional conformal models are examined.