The design of a distributed data base for a hierarchical computer system is investigated. If the transmission cost and storage cost can be calculated from linear cost functions, a data base can be decomposed based upon a simple figure of merit. Moreover, each file can be allocated individually. When the cost functions are nonlinear, a file allocation algorithm is proposed to allocate files which again is based upon a simple figure of merit. The decomposition problem for completely decentralized data bases is also considered.