Recently, the authors characterized all finite-dimensional square-free algebrasAover a fieldK, and gave a detailed description of their automorphism groups. Using the notion of rings with local units we now extend the definition of square-freealgebras to possibly infinite dimensional ones and observe that the earlier characterization carries over to the infinite dimensional case. Then relying on an appropriate version of the recent notion of inner automorphism introduced by Beattie and del Río, we extend the description of the automorphism groups to the enlarged class of square-free algebras.