In this note, we revisit the Θ-invariant as defined by R. Bott and the first author. The Θ-invariant is an invariant of rational homology 3-spheres with acyclic orthogonal local systems, which is a generalization of the 2-loop term of the Chern-Simons perturbation theory. The Θ-invariant can be defined when a cohomology group is vanishing. In this note, we give a slightly modified version of the Θ-invariant that we can define even if the cohomology group is not vanishing.
