The squeezed state, capable of the important quantum resource, has vast potential applications in quantum computing, quantum communications and precision measurement. In the noncritically squeezed light theory, the predicted noncritically squeezed light can be generated by the spontaneous rotational symmetry breaking occurring in a degenerate optical parametric oscillator (DOPO) pumped above threshold. The reliability of this kind of squeezing is crucially important, as its quantum performance is robust to the pump power in the experiment. However, the detected squeezing degrades rapidly in detection, because the squeezed mode orientation diffuses slowly which leads to a small mode mismatch during the homodyne detection. In this paper, we propose an experimentally feasible scheme to make the detection of noncritically squeezing reliable by employing the spatial mode swapping technic. Theoretically, the dynamic fluctuation aroused by random mode rotation in the squeezing detection can be compensated perfectly, and 3dB squeezing can be achieved robustly even with additional vacuum noise. Our scheme makes an important step for the experimental generation of noncritically squeezed light.