We propose a novel reliability estimation method which judges whether the recognition result is correct or erroneous in character recognition. To solve the problem, this paper have the problem of the reliability estimation return to the constraint satisfaction problems of maximizing the errorrejection rate when the own-category relief rate is given. To calculate the correct-acceptance rate and error-rejection rate, the technology of two thresholds used in the field of reject judgment is applied. Since this problem cannot be solved by an equation, this paper proposes a graphic solution. The formulation of the problem and the solution proposal are new. In an experiment using character patterns written in free style, reliability achieved a range from 0.802 to 0.819. Since the recognition rate was 74.8%, the value converted into the percentage of reliability exceeds the recognition rate. On the patterns estimated as correct recognition, the cumulative classification rates of top-1, top-2 and top-10 were 90.5%, 94.5% and 97.2%, respectively, and the occupation rate that is proportion of the patterns in entire patterns was 71.8%. The experimental results show the proposed method can extract only the high-quality character pattern whose recognition rate is 90.5% from among unknown patterns including a poor-quality character pattern whose recognition rate is 74.8%. These results confirm that the proposed method is effective against real world problems and is sufficient for practical application.