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Magnetic fields have an important role in the evolution of interstellar medium and star formation. As the only direct probe of interstellar field strength, credible Zeeman measurements remain sparse owing to the lack of suitable Zeeman probes, particularly for cold, molecular gas. Here we report the detection of a magnetic field of +3.8 ± 0.3 microgauss through the H I narrow self-absorption (HINSA) towards L1544—a well-studied prototypical prestellar core in an early transition between starless and protostellar phases characterized by a high central number density and a low central temperature. A combined analysis of the Zeeman measurements of quasar H I absorption, H I emission, OH emission and HINSA reveals a coherent magnetic field from the atomic cold neutral medium (CNM) to the molecular envelope. The molecular envelope traced by the HINSA is found to be magnetically supercritical, with a field strength comparable to that of the surrounding di use, magnetically subcritical CNM despite a large increase in density. The reduction of the magnetic fux relative to the mass, which is necessary for star formation, thus seems to have already happened during the transition from the di use CNM to the molecular gas traced by the HINSA. This is earlier than envisioned in the classical picture where magnetically supercritical cores capable of collapsing into stars form out of magnetically subcritical envelopes.