The currently available ²-lactamase inhibitors are insufficient to inhibit the incessantly increasing ²-lactamase, and novel ²-lactamase inhibitors has been required today for the difficult treatment for bacterial infectious diseases caused by resistant bacteria which produce class C ²-lactamase, extended-spectrum ²-lactamase (ESBL) belonging to class A and D, or class A KPC-2 decomposing even carbapenem as a last resort for ²-lactam antibiotic. A compound represented by the the formula (I), preparation process of the same, ²-lactamase inhibitors and method for treating bacterial infectious diseases are provided.