This paper addresses fractional cell formation in Group Technology implementation, where part of the production facility is redesigned into manufacturing cells. The fractional cell formation issue is important in manufacturing cell design, because it may not be possible to economically convert the entire facility to manufacturing cells. The authors discuss the issues in modeling fractional cell formation problems and they develop efficient algorithms to group the facilities into manufacturing cells and a remainder cell. Algorithms are tested using a variety of matrices including those from real-life situations to demonstrate the potential applicability of the proposed approach. Significance: Fractional cell formation is an emerging concept that is useful to minimize inter-cell moves in Cellular manufacturing applications. The algorithms and methods proposed in this paper have the potential to reduce the cost of implementation while substantially increasing the product throughput times.