  Foreground removal is a challenge for 21-cm tomography of the high redshift
Universe. We use archival GMRT data (obtained for completely different
astronomical goals) to estimate the foregrounds at a redshift ~ 1. The
statistic we use is the cross power spectrum between two frequencies separated
by \Delta{\nu} at the angular multipole l, or equivalently the multi-frequency
angular power spectrum C_l(\Delta{\nu}). An earlier measurement of
C_l(\Delta{\nu}) using this data had revealed the presence of oscillatory
patterns along \Delta{\nu}, which turned out to be a severe impediment for
foreground removal (Ghosh et al. 2011). Using the same data, in this paper we
show that it is possible to considerably reduce these oscillations by
suppressing the sidelobe response of the primary antenna elements. The
suppression works best at the angular multipoles l for which there is a dense
sampling of the u-v plane. For three angular multipoles l = 1405, 1602 and
1876, this sidelobe suppression along with a low order polynomial fitting
completely results in residuals of (\leq 0.02 mK^2), consistent with the noise
at the 3{\sigma} level. Since the polynomial fitting is done after estimation
of the power spectrum it can be ensured that the estimation of the HI signal is
not biased. The corresponding 99% upper limit on the HI signal is xHI b \leq
2.9, where xHI is the mean neutral fraction and b is the bias.
