  In this paper we characterise with the matrix the complete flag of riemannian
extension (see d\'efinition) on a riemannian compact manifold whose metric is
bundlelike for any foliation F_{s} of this flag. This study show us that a
foliation of a complete flag of riemannian extension on a riemannian compact
manifold whose metric is bundlelike for any foliation of this flag is a
transversely diagonal riemannian foliation (see d\'efinition).
