A projection \(P\) on a given Banach space \(X\) is said to be generalized bi-circular if \(P+\lambda(I-P)\) is an isometry for some number \(\lambda\neq 1\) in the unit circle of the complex plane (see M. Fošner et al. [Linear Algebra Appl. 420, No. 2–3, 596–608 (2007; Zbl 1110.15025)]). The authors obtain the standard form of generalized bi-circular projections in the Banach space \(C_0(\Omega,X)\), with \(\Omega\) a locally compact Hausdorff space (not necessarily connected) and \(X\) a Banach space with trivial centralizer, and give several examples showing, in particular, that there are generalized bi-circular projection which cannot be written as the average of the identity with an isometric reflection.