We report the magnetic field-amplitude and field-angle dependence of the superconducting onset temperature Tc_onset of the organic superconductor (TMTSF)2ClO4 in magnetic fields H accurately aligned to the conductive ab plane. We revealed that the rapid increase of the onset fields at low temperatures occurs both for H // b and H // a, irrespective of the carrier confinement. Moreover, in the vicinity of the Pauli limiting field, we report a shift of a principal axis of the in-plane field-angle dependence of Tc_onset away from the b axis. This feature may be related to an occurrence of Fulde-Ferrell-Larkin-Ovchinnikov phases.
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