  We present new conditions that characterize the componentwise linearity of
Stanley-Reisner ideal of broken circuit complexes of simple matroids. We employ
the notion of graded linearity (called also quasilinearity in the literature),
which is more general than having linear resolution and show that componentwise
linearity is equivalent to have graded linear resolution. As a result
generalizing the one in \cite{RV}, we prove that the componentwise linearilty
of Stanley-Reisner ideal of broken circuit complex translates to the
decomposition of the matroid into specific matroids. An application to the
Koszul property of Orlik-Terao ideal of hyperplane arrangements is given. We
end up with some partial results on Koszul property and complete intersection
of Orlik-Terao algebra of central arrangements.
