In this paper, we consider the unequal error protection (UEP) for progressive image transmission when the coded packet size is fixed. First, we prove that, for the source code with convex rate-distortion (R-D) function and practically used channel codes, the channel code rate for each packet in the optimal rate allocation is nondecreasing indeed. Then, we give an upper bound for the channel code rate of the last packet so that the number of rate allocations in the exhaustive search can be predicted. Further, we propose a heuristic optimization method which has low complexity and obtains performance approaching to the optimal solutions for various channel conditions and transmission rates.