  We give in this paper a new construction of factors of type ${\rm III_1}$.
Under certain assumptions, we can, thanks to a result by Popa, give a complete
classification for this family of factors. Although these factors are never
full, we can nevertheless, in many cases, compute Connes' $\tau$ invariant. We
obtain a new example of an uncountable family of pairwise non-isomorphic
factors of type ${\rm III_1}$ with the same $\tau$ invariant.
