We used femtosecond nearly degenerate four-wave mixing (nDFWM) to measure the instantaneous third-order nonlinear optical susceptibility function chi (1111)[-(omega - delta tau), omega, omega, -(omega + delta omega)] near the absorption edge of C-60 films with absorption reaching up to 2.0 x 10(4) cm(-1). The frequency shift was set to h delta omega = 0.07 +/- 0.01 eV, smaller than the width of the spectral feature studied but large enough to suppress non-instantaneous signal contributions. Our data are orders of magnitude below previous DFWM results but connect smoothly to data at longer wavelengths where absorption is low (<100 cm(-1)).