Аннотация:The present paper continues the series of publications by the authors devoted to solvingthe problem of recognition regions with potential high seismicity. It is aimed at the development ofthe mathematical apparatus and the algorithmic base of the FCAZ method, designed for effectiverecognition of earthquake-prone areas. A detailed description of both the mathematical algorithmsincluded in the FCAZ in its original form and those developed in this paper is given. Using Californiaas an example, it is shown that a significantly developed algorithmic FCAZ base makes it possibleto increase the reliability and accuracy of FCAZ recognition. In particular, a number of small zoneslocated at a fairly small distance from each other but having a close “internal” connection are beingconnected into single large, high-seismicity areas.