  The frequency of barred spiral galaxies as a function of redshift contains
important information on the gravitational influence of stellar disks in their
dark matter halos and also may distinguish between contemporary theories for
the origin of galactic bulges. In this paper we present a new quantitative
method for determining the strength of barred spiral structure, and verify its
robustness to redshift-dependent effects. By combining galaxy samples from the
Hubble Deep Field North with newly available data from the Hubble Deep Field
South, we are able to define a statistical sample of 18 objectively-defined
low-inclination barred spiral systems with $I_{814W}<23.2$ mag. Analysing the
proportion of barred spiral galaxies seen as a function of redshift, we find a
significant decline in the barred fraction beyond redshifts $z\simeq 0.5$. The
physical significance of this effect remains unclear, but several possibilities
include dynamically hotter (or increasingly dark-matter dominated)
high-redshift discs, or an enhanced efficiency in bar destruction at high
redshifts. By investigating the formation of the ``orthogonal'' axis of
Hubble's classification tuning fork, our result complements studies of
evolution in the early--late sequence, and pushes to later epochs the redshift
at which the Hubble classification sequence is observed to be in place.
