  We constrain the primordial non-Gaussianity parameter of the local model
f_{NL} using the skewness power spectrum associated with the two-to-one
cumulant correlator of cosmic microwave background temperature anisotropies.
This bispectrum-related power spectrum was constructed after weighting the
temperature map with the appropriate window functions to form an estimator that
probes the multipolar dependence of the underlying bispectrum associated with
the primordial non-Gaussianity. We also estimate a separate skewness power
spectrum sensitive more strongly to unresolved point sources. When compared to
previous attempts at measuring the primordial non-Gaussianity with WMAP data,
our estimators have the main advantage that we do not collapse information to a
single number. When model fitting the two-to-one skewness power spectrum we
make use of bispectra generated by the primordial non-Gaussianity, radio point
sources, and lensing-secondary correlation. We analyze Q, V and W-band WMAP
5-year data using the KQ75 mask out to l_{max}=600. Using V and W-band data and
marginalizing over model parameters related to point sources and
lensing-secondary bispectrum, our overall and preferred constraint on f_{NL} is
11.0\pm23.7 at the 68% confidence level (-36.4 < f_{NL} < 58.4 at 95%
confidence). We find no evidence for a non-zero value of f_{NL} even marginally
at the 1\sigma level.
