  A class of axial decomposition algebras with Miyamoto group generated by two
Miyamoto automorphisms and three eigenvalues $0,1$ and $\eta$ is introduced and
classified in the case with $\eta\notin\{0,1,\frac{1}{2}\}$. This class
includes specializations of 2-generated axial algebras of Majorana type
$(\xi,\eta)$ to the case with $\xi=\eta$.
