  We factorize 4d Fradkin-Linetsky higher spin conformal algebra by maximal
ideal $I^1-\alpha$ and construct irreducible infinite-dimensional modules
$M_\alpha$ of 4d conformal algebra that are parameterized by real number
$\alpha$. It is shown that independently of $\alpha$ unfolded system of
equations corresponding to each $M_\alpha$ describes collection of
Fradkin-Tseytlin equations for all spins $s=1,\dots,\infty$ with zero
multiplicity.
