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

De la caract\'erisation matricielle des drapeaux complets d'extensions  riemanniennes aux feuilletages riemanniens transversalement diagonaux sur une  vari\'et\'e compacte connexe