  The hierarchy of conformally coupled scalars with the increasing scaling
dimensions $\Delta_{k}=k-d/2$, $k=1,2,3,... $ connected with the $k$-th Euler
density in the corresponding space-time dimensions $d\geq 2k$ is proposed. The
corresponding conformal invariant Lagrangian with the $k$-th power of Laplacian
for the already known cases $k=1,2$ is reviewed, and the subsequent case of
$k=3$ is completely constructed and analyzed.
