  In this paper we introduce and show some new notions and results on cg-frames
of Hilbert spaces. We define cg-orthonormal bases for a Hilbert space H and
verify their properties and relations with cg-frames. Actually, we present that
every cg-frame can be represented as a composition of a cg-orthonormal basis
and an operator under some conditions. Also, we find for any cg-frame an
induced c-frame and study their properties and relations. Moreover, we show
that every cg-frame can be written as aggregate of two Parseval cg-frames. In
addition, We show each cg-frame as a summation of a cg-orthonormal basis and a
cg-Riesz basis.
