The problem of generating constrained cutting patterns for rectangular blanks of a single size from a rectangular sheet by a joining method was dealt with. A branch and bound method has been used to extend the tree of patterns, and all nodes possible to improve the current best solution were explored. The methods to branch and to obtain upper and lower bounds were described in detail. Agrawal's algorithm for generating unconstrained patterns was extended to generate constrained patterns. The joining algorithm and the extended Agrawal's algorithm have been applied to the same group of experimental data. The computational results showed that the joining algorithm is extremely efficient.