We examine the use of the CMBs 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 $2sigma$ 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.
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