An angle-resolved photoemission study is reported on Ca2CUO2Cl2, a parent compound of high-T-c 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 \cosk(x)a - cosk(y)a\ 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.