ln this paper, a new two-dimensional (2-D) searching flow scheme is proposed for the incremental backprojection algorithm [9]. In this scheme, the searching direction in a beam is determined only by the distance value of the current pixel to the corresponding ray; no pixeis outside the beam are involved in the procedure. In addition, the geometrical relationships between the image grids and the projection rays in different views are fully exploited to further reduce the searching operations. It is found that backprojection of four views, θ,π/2-θ,π/2+θ, and π-θ, can be performed at the same time, and the searching operation is only required for one of them if the number of views is even. Thus, backprojection is accomplished on a quartet-by-quartet basis of views as well as on a beam-by-beam basis. Our approaches not only minimize the number of searching operations but also possess a simple algorithm structure. Implementation results on an AST-386 computer for the incremental backprojection algorithm by using this new searching flow scheme and the relationship among projection views show that the processing time can be reduced by a factor of about 2, compared with the original method.