The radical pair mechanism is an important model that may provide a basis for biological magnetoreception. To account for the high orientation precision of the real avian compass, P. J. Hore et al. proposed an intriguing phenomenon called quantum needle [Proc. Natl. Acad. Sci. 113, 4634 (2016)], where a spike-like feature emerges in the fractional yield signal. However, it is believed that quantum needle requires the radical pair lifetime to be longer than a few microseconds and thus poses stern challenges in realistic biological systems. Here, we exploit the optimization techniques and find a novel class of model system, which sustains much more prominent features of quantum needle and significantly relaxes the requirement for radical pair lifetime. Even more surprisingly, we find that the characteristics of quantum needle retain a narrow functional window around the geomagnetic field, which is absent in the previous model systems. Therefore, our work provides essential evidence for identifying the possible physical mechanism for quantum needle in chemical magnetoreception.