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We propose a novel method for building <inline-formula> <tex-math notation="LaTeX">${N}$ </tex-math></inline-formula>-port nonblocking optical switches on a silicon chip. The rationale behind this is a bidirectional merge-replace-mirror method. It offers nonblocking interconnections among multiple inputs and outputs. The critical merits include <inline-formula> <tex-math notation="LaTeX">$170~\mu \text{m}\,\,\times 300~\mu \text{m}$ </tex-math></inline-formula> footprint, nano-second circuit-switching, and <inline-formula> <tex-math notation="LaTeX">$85.1~\mu \text{W}$ </tex-math></inline-formula> power consumption per link. The worst-case on-chip insertion loss for the 32-port optical switch is 18.02dB (all cross) and crosstalk is &#x2212;16.96dB (all bars), respectively.