Improving the performance of a database system is one of the key research issues now a day. Distributed processing is an effective way to improve reliability and performance of a database system. Distribution of data is a collection of fragmentation, allocation and replication processes. Previous research works provided fragmentation solution based on empirical data about the type and frequency of the queries submitted to a centralized system. These solutions are not suitable at the initial stage of a database design for a distributed system. In this paper we have presented a fragmentation technique that can be applied at the initial stage as well as in later stages of a distributed database system for partitioning the relations. Allocation of fragments is done simultaneously in our algorithm. Result shows that proposed technique can solve initial fragmentation problem of relational databases for distributed systems properly.