We investigated the propagation of femtosecond laser pulses through a metamaterial that has a negative index of refraction for wavelengths around 1.5 micrometers. From the interference fringes of a Michelson interferometer with and without the sample, we directly inferred the phase time delay. From the pulse-envelope shift, we determined the group time delay. In a spectral region, phase and group velocity are negative simultaneously. This means that both the carrier wave and the pulse envelope peak of the output pulse appear at the rear side of the sample before their input pulse counterparts have entered the front side of the sample.