theory. A closer look at the conformal Ward identities (CWI) in LO for the flavour non-singlet channel [@Mue91; @Mue94], which include both dilatation and special conformal transformations, shows that the conformal covariance is destroyed in the minimal subtraction scheme (${\overline{\rm MS}}$) by an off-diagonal special conformal anomaly matrix $\hat{\gamma}^c(l)=\{\gamma^c_{jj'}(l)\}$, which depends on the spin $l$ carried by the considered twist-2 operator. To restore it to all orders of perturbation theory one is forced to perform a finite renormalization of the conformal operators leading to the conformal subtraction (CS) scheme. Assuming a non-trivial fixed point $g^*$, i.e. that $\beta (g^*)$ is zero, this restoration is assured in any order of the perturbation theory by conformal constraints which arise from the algebra of the collinear conformal group: $$\begin{aligned}
\label{conf-constr-KD-1}
\left[ D , K_- \right]_- &=& iK_-
\hspace{2.7cm} \Longrightarrow \hspace{1cm} \left[ \hat a (l)
+ \hat \gamma ^c(l), \hat \gamma \right] = 0, \\
\label{conf-constr-KD-2}
\left[ P_+ , K_- \right]_- &=&
2i( D + M_{-+} )\hspace{1cm} \Longrightarrow \hspace{1cm}
\hat \gamma ^c (l+1) - \hat \gamma ^c (l) = - 2 \hat \gamma ,\end{aligned}$$ where $a_{jj'}(l)= a(j,l) \cdot \delta_{jj'}$ and $a(j,l)
\equiv 2(j-l)(j+l+3)$. For the case of $\phi^3_{(6)}$ theory, this constraints can be extended 