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The superconducting transmon qubit is currently a leading qubit modality for quantum computing, but gate performance in quantum processor with transmons is often insufficient to support running complex algorithms for practical applications. It is thus highly desirable to further improve gate performance. Due to the weak anharmonicity of transmon, a static ZZ interaction between coupled transmons commonly exists, undermining the gate performance, and in long term, it can become performance limiting. Here we theoretically explore a previously unexplored parameter region in an all-transmon system to address this issue. We show that an feasible parameter region, where the ZZ interaction is heavily suppressed while leaving XY interaction with an adequate strength to implement two-qubit gates, can be found for all-transmon systems. Thus, two-qubit gates, such as cross-resonance gate or iSWAP gate, can be realized without the detrimental effect from static ZZ interaction. To illustrate this, we demonstrate that an iSWAP gate with fast gate speed and dramatically lower conditional phase error can be achieved. Scaling up to large-scale transmon quantum processor, especially the cases with fixed coupling, addressing error, idling error, and crosstalk that arises from static ZZ interaction could also be strongly suppressed.