  In this article, we consider the multiarrangements whose underlying
arrangements are the Coxeter arrangement of type $B_2$. For some special
multiplicities, we give an explicit description of bases for the derivation
modules. As an application, we also describe the lower derivations of bases for
the derivation modules of some Coxeter multiarrangements of type $A_2$, which
are different from ones given by Wakamiko.
