  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.
