  We study the algebraic features of covariant tensors of valence four
containing two blocks of skew indices. After a rather general treatment, we
specialize ourselves to four-dimensional spacetimes and discuss several
complementary aspects of these objects. In particular, we focus our attention
on the corresponding invariant subspaces and generalise previous relations such
as the Ruse-Lanczos identity, the Bel-Matte decomposition and the Lovelock-like
quadratic identities. We conclude pointing out some possible applications of
the formalism.
