  The purpose of this paper is to establish a non-integrated defect relation
for meromorphic mappings from a complete K\"{a}hler manifold into a projective
variety intersecting an arbitrary family of hypersurfaces with explicit
truncation level. In our result, both the total defect and the truncation level
are estimated independently of the number of involving hypersurfaces. Our
result generalizes and improves the previous results in this topic.
