  We construct a coalescence hidden variable fractal interpolation function
(CHFIF) through a non-diagonal iterated function system(IFS). Such a FIF may be
self-affine or non-self-affine depending on the parameters of the defining
non-diagonal IFS. The smoothness analysis of the CHFIF has been carried out by
using the operator approximation technique. The deterministic construction of
functions having order of modulus continuity O (|t|^{delta} (log|t|)^m), (m a
non-negative integer and 0 < delta le 1) is possible through our CHFIF. The
bounds of fractal dimension of CHFIFs are obtained first in certain critical
cases and then, using estimation of these bounds, the bounds of fractal
dimension of any FIF are found.
