  In this paper, we introduce a strongly quasi-local version of the coarse
Novikov conjecture, which states that certain assembly map from the coarse
$K$-homology of a metric space to the $K$-theory of its strongly quasi-local
algebra is injective. We prove that the conjecture holds for metric spaces with
bounded geometry which can be coarsely embedded into Banach spaces with
Property (H), introduced by Kasparov and Yu. Besides, we also generalise the
notion of strong quasi-locality to proper metric spaces and provide a
(strongly) quasi-local picture for $K$-homology.
