  Rehren proved that a primitive 2-generated axial algebra of Monster type
$(\alpha,\beta)$ has dimension at most eight if
$\alpha\notin\{2\beta,4\beta\}$. In this note we construct an
infinite-dimensional 2-generated primitive axial algebra of Monster type
$(2,\frac{1}{2})$ over an arbitrary field $F$ with $char(F)\neq 2,3$. This
shows that the second special case, $\alpha=4\beta$, is a true exception to
Rehren's bound.
