  We present new constraints on the non-linear coupling parameter fnl with the
Wilkinson Microwave Anisotropy Probe (WMAP) data. We use an updated method
based on the spherical Mexican hat wavelet (SMHW) which provides improved
constraints on the fnl parameter. This paper is a continuation of a previous
work by Curto et al. where several third order statistics based on the SMHW
were considered. In this paper, we use all the possible third order statistics
computed from the wavelet coefficient maps evaluated at 12 angular scales. The
scales are logarithmically distributed from 6.9 arcmin to 500 arcmin. Our
analysis indicates that fnl is constrained to -18 < fnl < +80 at 95% confidence
level (CL) for the combined V+W WMAP map. This value has been corrected by the
presence of undetected point sources, which adds a positive contribution of
Delta_fnl = 6 +- 5. Our result excludes at ~99% CL the best-fitting value
fnl=87 reported by Yadav & Wandelt. We have also constrained fnl for the Q, V
and W frequency bands separately, finding compatibility with zero at 95 % CL
for the Q and V bands but not for the W band. We have performed some further
tests to understand the cause of this deviation which indicate that systematics
associated to the W radiometers could be responsible for this result. Finally
we have performed a Galactic North-South analysis for fnl. We have not found
any asymmetry, i.e. the best-fitting fnl for the northern pixels is compatible
with the best-fitting fnl for the southern pixels.
