Abstract A suspension of a map consists of the flow for which the Poincare section is that map. Designing a suspension of a given map remains a non-trivial task in general. The case of suspending the Henon map is here considered. Depending on the parameter values, the Henon map is orientation preserving or reversing; it is here shown that while a tridimensional suspension can be obtained in the former case, a four-dimensional flow is required to suspend the latter. A topological characterization of the three-dimensional suspension proposed by Starrett and Nicholas for the orientation preserving area is performed. A template is proposed for the four-dimensional case, for which the governing equations remain to be obtained.