Prediction programs for general PCR (or random PCR) products had been developed [3, 2]. These programs had been experimentally shown to be highly accurate in its prediction [2]. On the other hand, random PCR have been demonstrating that it is very useful as an elementary technology of genome profiling [1], in which random PCR products (a set of DNA fragments extracted from various parts of genomic DNA) are subjected to TGGE (temperature gradient gel electrophoresis), generating a set of characteristic band patterns (see Fig. 1), for identification of species [4]. So far as the identification of species is concerned, any sequence of primer is usable for genome profiling (GP). However, in some cases availability of a particular DNA fragment of known sequence makes GP analysis highly informative as in the case where the verotoxin genome responsible for HUS (Haemolytic Uraemic Syndrome) is contained in the genome of a test strain of E. coli. For this purpose, the single probe oligonucleotide used for random PCR should be designed to be able to replicate a particular sequence such as a verotoxin and a 16S rRNA genes. This constitutes an ‘inverse random PCR problem’, of which the normal one is to find the products specified by an oligonucleotide.