An angle-resolved photoemission study is reported on Ca2CuO2Cl2, a parent compound of high-Tc superconductors. Analysis of the electron occupation probability, n(k), from the spectra shows a steep drop in spectral intensity across a contour that is close to the Fermi surface predicted by the band calculation. This analysis reveals a Fermi surface remnant, even though Ca2CuO2Cl2 is a Mott insulator. The lowest energy peak exhibits a dispersion with approximately the &cjs3539;coskxa - coskya&cjs3539; form along this remnant Fermi surface. Together with the data from Dy-doped Bi2Sr2CaCu2O8+delta, these results suggest that this d-wave-like dispersion of the insulator is the underlying reason for the pseudo gap in the underdoped regime.