  The relationship between dust polarization and extinction was determined for
the cold dense starless molecular cloud core FeSt 1-457 based on the background
star polarimetry of dichroic extinction at near-infrared wavelengths. Owing to
the known (three-dimensional) magnetic field structure, the observed
polarizations from the core were corrected by considering (a) the subtraction
of the ambient polarization component, (b) the depolarization effect of
inclined distorted magnetic fields, and (c) the magnetic inclination angle of
the core. After these corrections, a linear relationship between polarization
and extinction was obtained for the core in the range up to $A_V \approx 20$
mag. The initial polarization vs. extinction diagram changed dramatically after
the corrections of (a) to (c), with the correlation coefficient being refined
from 0.71 to 0.79. These corrections should affect the theoretical
interpretation of the observational data. The slope of the finally obtained
polarization--extinction relationship is $P_H / E_{H-K_s} = 11.00 \pm 0.72$
$\%$ ${\rm mag}^{-1}$, which is close to the statistically estimated upper
limit of the interstellar polarization efficiency (Jones 1989). This
consistency suggests that the upper limit of interstellar polarization
efficiency might be determined by the observational viewing angle toward
polarized astronomical objects.
