  The binary fraction among extreme horizontal branch (EHB) stars in Galactic
globular clusters (GCs) is an order of magnitude lower than the binary fraction
among their counterparts, field hot subdwarfs. This casts serious doubt on
their formation channels. In this {\em Letter}, I explain the difference
between the field and the cluster EHB stars with the binary model of Han et al.
(2002, 2003) for the formation of EHB stars. With the binary population
synthesis code of Han et al. (2002, 2003), I follow the evolution of simple
stellar populations resulting from single star bursts (note that Han et al.
2002, 2003, adopted a constant star formation rate over the last 15 Gyr for the
production of field EHB stars), and obtain EHB stars at different stellar
population ages. I found that the binary fraction among EHB stars decreases
with the stellar population age. The fraction of EHB binaries with orbital
periods $P<5 {\rm d}$ is $\sim 2.5%$ for a stellar population of 10 Gyr from
the standard simulation set. The binary model of Han et al. (2002, 2003) is
able to explain the lack of EHB binaries in globular clusters. I also propose
that the precise determination of the physical parameters of close EHB binaries
in GCs can lead to the strictest constraint on common-envelope ejection
efficiency.
