  Riemann tensor irreducible part $E_{iklm} = {1/2} (g_{il}S_{km} +
g_{km}S_{il} - g_{im}S_{kl} - g_{kl}S_{im})$ constructed from metric tensor
$g_{ik}$ and traceless part of Ricci tensor $S_{ik} = R_{ik} - {1/4} g_{ik} R$
is expanded into bilinear combinations of bivectorial fields being
eigenfunctions of $E$. Field equations for the bivectors induced by Bianchi
identities are studied and it is shown that in general case it will be
3-parametric local symmetry group Yang-Mills field.
