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We report a search for the decays $B^0\to K^{*0} \overline{K}{}^{*0}$ and$B^0\to K^{*0} K^{*0}$. We also measure other charmless decay modes with$K^+\pi^-K^-\pi^+$ and $K^{+}\pi^{-}K^{+}\pi^{-}$ final states. The results areobtained from a data sample containing $657 \times 10^6$ $B \overline B$ pairscollected with the Belle detector at the KEKB asymmetric-energy $e^+e^-$collider. We set upper limits on the branching fractions for $B^0\to K^{*0}\kstarbar$ and $B^0\to K^{*0} K^{*0}$ of $0.81 \times 10^{-6}$ and $0.20\times10^{-6}$, respectively, at the 90% confidence level.

Search for $B^0 \to K^{*0} \overline{K}{}^{*0}$, $B^0 \to K^{*0} K^{*0}$ and $B^0 \to K^+\pi^- K^{\mp}\pi^{\pm}$ Decays

Search for $B^0 \to K^{0} \overline{K}{}^{0}$, $B^0 \to K^{0} K^{0}$ and $B^0 \to K^+\pi^- K^{\mp}\pi^{\pm}$ Decays