Rehren proved in Axial algebras. Ph.D. thesis, University of Birmingham (2015), Trans Am Math Soc 369:6953–6986 (2017) that a primitive 2-generated axial algebra of Monster type (alpha ,beta ), over a field of characteristic other than 2, has dimension at most 8 if alpha notin {2beta ,4beta }. In this note, we show that Rehren’s bound does not hold in the case alpha =4beta by providing an example (essentially the unique one) of an infinite-dimensional 2-generated primitive axial algebra of Monster type (2,frac{1}{2}) over an arbitrary field {{mathbb {F}}} of characteristic other than 2 and 3. We further determine its group of automorphisms and describe some of its relevant features.