Let A be a complex unital Banach algebra with unit 1. An element a∈ A is said to be of G1-class if ‖(z-a)-1‖=1d(z,σ(a))∀z∈C\σ(a).Here d(z, σ(a)) denotes the distance between z and the spectrum σ(a) of a. Some examples of such elements are given and also some properties are proved. It is shown that a G1-class element is a scalar multiple of the unit 1 if and only if its spectrum is a singleton set consisting of that scalar. It is proved that if T is a G1 class operator on a Banach space X, then every isolated point of σ(T) is an eigenvalue of T. If, in addition, σ(T) is finite, then X is a direct sum of eigenspaces of T. © 2022, The Author(s), under exclusive licence to The Forum D’Analystes.