Chaotic signals with a flat power spectrum over 20 GHz have been generated using two commercially available semiconductor lasers coupled in a unidirectional master-slave scheme. The master laser has an external optical feedback that induces optical chaos in the laser output. A part of the chaotic light output from the master laser is injected into the slave laser. We experimentally demonstrated the generation of broad-band signals up to 22 GHz using lasers whose relaxation oscillation frequency in the free-running state is only around 6.4 GHz. We also show that the experimental results can be well reproduced by numerical simulations using two coupled rate equations. The numerical investigation shows that the high-frequency broad-band signal generation is owing to two key effects: high-frequency oscillations as a result of beating between the master and slave laser lights, and spectrum flattening due to the injection of the chaotic signal. The flatness, stability, and tunability of the power spectra demonstrated in our experiments suggests that the proposed system can be potentially useful for generation of high-frequency broad-band random signals.