  This paper studies a variant of Horrocks criteria for vector bundles mainly
through a syzygy theoretic approach. In this spirit we begin with describing
various proofs of the splitting criteria for ACM and Buchsbaum bundles, giving
new sights of the structure theorem. Our main result gives a structure theorem
of quasi-Buchsbaum bundles on ${\mathbb P}^n$, which characterizes the
null-correlation bundle. Also, the quasi-Buchsbaum bundles on ${\mathbb P}^3$
with simple cohomologies are classified in terms of standard system of
parameters.
