  We examine the use of the CMB's TE cross correlation power spectrum as a
complementary test to detect primordial gravitational waves (PGWs). The first
method used is based on the determination of the lowest multipole, $\ell_0$,
where the TE power spectrum, $C_{\ell}^{TE}$, first changes sign. The second
method uses Wiener filtering on the CMB TE data to remove the density
perturbations contribution to the TE power spectrum. In principle this leaves
only the contribution of PGWs. We examine two toy experiments (one ideal and
another more realistic) to see their ability to constrain PGWs using the TE
power spectrum alone. We found that an ideal experiment, one limited only by
cosmic variance, can detect PGWs with a ratio of tensor to scalar metric
perturbation power spectra $r=0.3$ at 99.9% confidence level using only the TE
correlation. This value is comparable with current constraints obtained by WMAP
based on the $2\sigma$ upper limits to the B-mode amplitude. We demonstrate
that to measure PGWs by their contribution to the TE cross correlation power
spectrum in a realistic ground based experiment when real instrumental noise is
taken into account, the tensor-to-scalar ratio, $r$, should be approximately
three times larger.
