Schmidt telescopes currently provide nearly the only means to obtain positi
ons of faint objects with respect to the standard ICRS reference system. Ho
wever, the lack of adequate astrometric calibration methods to account for
the specific properties of Schmidt telescopes leads to residual systematic
errors of up to 1". The main source of systematic errors is plate bending d
uring exposure. A high-precision reduction technique to account for this ef
fect is proposed. Application of this technique to observations acquired wi
th the Schmidt telescopes of the Palomar and Anglo-Australian Observatories
reduced the systematic errors by a factor of 2.5 and gave them a simpler s
tructure, while simultaneously decreasing the number of unknowns in the red
uction model threefold. Application of the new method, with appropriate acc
ount for the design of the particular plateholder used, will make it possib
le to use Schmidt telescopes to determine high-precision positions for virt
ually all objects detected in photographic surveys. (C) 2000 MAIK "Nauka/In
terperiodica".