Tissue background suppression is essential for harmonic detection of ultrasonic contrast microbubbles. To reduce the tissue harmonic amplitude for improvement of contrast-to-tissue ratio (CTR), the method of third harmonic (3f(0)) transmit phasing uses an additional 3f(0) transmit signal to provide mutual cancellation between the frequency-sum component and the frequency-difference component of tissue harmonic signal. Chirp excitation can further improve the SNR in harmonic imaging without requiring an excessive transmit pressure and thus reduce potential bubble destruction. However, for effective suppression of tissue harmonic background in 3f(0) transmit phasing, the 3f(0) chirp waveform has to be carefully designed for the generation of spectrally matched cancellation pairs over the entire second harmonic band. In this study, we proposed a chirp waveform suitable for the method of 3f(0) transmit phasing, the different-bandwidth chirp signal (DBCS). With the DBCS waveform, the frequency-difference component of tissue harmonic signal becomes a chirp signal similar to its frequency-sum counterpart. Thus, the combination of the DBCS waveform with the 3f(0) transmit phasing can markedly suppress the tissue harmonic amplitude for CTR improvement together with effective SNR increase of contrast harmonic signal. Our results indicate that, as compared with the conventional Gaussian pulse, the DBCS waveform can provide 6-dB improvement of SNR in 3f(0) transmit phasing with a CTR increase of 3 dB. Nevertheless, the limitation of available transmit bandwidth and the frequency-dependent attenuation can degrade the performance of the DBCS waveform in tissue suppression. The design of the DBCS waveform is also applicable to other dual-frequency imaging techniques that rely on the harmonic generation at the difference frequency.