  We determined the crystal structure of Ba$_2$CoSi$_2$O$_6$Cl$_2$, which was
synthesized in this work, and investigated its quantum magnetic properties
using single crystals. This compound should be described as a two-dimensionally
coupled spin-1/2 XY-like spin dimer system. Ba$_2$CoSi$_2$O$_6$Cl$_2$ exhibits
a stepwise magnetization process with a plateau at half of the saturation
magnetization, irrespective of the field direction, although all the Co$^{2+}$
sites are equivalent. This indicates that spin triplets are localized owing to
the almost perfect frustration of interdimer exchange interactions. Thus, the
spin states for the zero and 1/2 magnetization-plateau states are almost
exactly given by the simple product of singlet dimers and the alternate product
of singlet and triplet dimers, respectively.
