  A squaregraph is a plane graph in which each internal face is a $4$-cycle and
each internal vertex has degree at least 4. This paper proves that every
squaregraph is isomorphic to a subgraph of the semi-strong product of an
outerplanar graph and a path. We generalise this result for infinite
squaregraphs, and show that this is best possible in the sense that
"outerplanar graph" cannot be replaced by "forest".
