This note is the sequel to the author's paper [\textit{N. F. Palinchak}, Math. Notes 55, No. 5, 512-516 (1994); translation from Mat. Zametki 55, No. 5, 110-115 (1994; Zbl 0852.14015)]. Quadrics all of whose linear automorphisms are of the form \(z \mapsto\mu z , w\mapsto |\mu|^2 w, \mu\in\mathbb C \setminus\{0\}\) were called \(c\)-rigid by \textit{V. K. Beloshapka} [Math. USSR, Sb. 72, No. 1, 189-205 (1992); translation from Mat. Sb. 182, No. 2, 203-219 (1991; Zbl 0724.32011)]. The main result of the note is the following: Any \(c\)-rigid strongly nondegenerate \((k, n)\)-quadric has no nonlinear automorphisms. A table indicating the relationship between linear and nonlinear automorphisms for \((k, n)\)-quadrics and an example for each case from this table are presented.