A submanifold \(N\) in a Riemannian manifold \(M\) is called totally umbilical if its second fundamental form is proportional to the first fundamental form. In this note, the author continues the study of totally umbilical submanifolds in symmetric spaces. In [the author, Mat. Fiz. Anal. Geom. 1, 314-357 (1994; Zbl 0841.53047)] totally umbilical submanifolds of dimension greater than 2 were completely classified. However, the case \(n=2\) appeared to be substantially more complicated, especially for symmetric spaces other than two-point homogeneous. In three previous papers [the author, Ukr. Geom. Sb. 34, 83-98 (1991; Zbl 0763.53058); 35, 83-99 (1992; Zbl 0833.53046); and Mat. Fiz. Anal. Geom. 3, 339-355 (1996; Zbl 0894.53047)] the classification of totally umbilical two-dimensional submanifolds in the Grassmann manifold \(G(2,n)\) was given. The present note contains some technical results and lemmas needed for the proof.