The Ribaucour transformation is applied to the family of Lagrangian submani
folds of dimension n and nonzero constant sectional curvature c of complex
space forms of complex dimension n and constant holomorphic sectional curva
ture 4c. As a consequence, a process is obtained to generate a new family o
f such submanifolds starting from a given one. In particular, explicit para
metrizations in terms of elementary functions of examples with arbitrary di
mension are curvature are provided. A permutability formula is derived whic
h provides a simple algebraic procedure to construct further examples once
two Ribaucour transforms of a given submanifold are known. The analytical c
ounterparts of the above results are also discussed.