A new analysis method is introduced for investigating whether major flares are clustered in certain fixed regions of the Sun in rigidly rotating coordinate systems. This method is applied to the analysis of major flares of solar cycles 19-23. The northern and southern hemispheres are separately analyzed, and it is found that longitude distributions of flares in the two hemispheres are different. Therefore, the term "hot spot" is used instead of "active longitude." Seven hot-spot systems are found to be significant, with their rotation periods ranging from 25 to 29 days. Four of them are single-hot-spot systems, and the remaining three are double-hot-spot systems. A double-hot-spot system is made of two hot spots that rotate with the same period but are separated by about 180° in longitude. The most significant hot-spot system is the double-hot-spot system with a period of 26.73 days that operated in the northern hemisphere during cycles 20 and 21. It was previously detected by the analysis of flare data of cycles 20 and 21. Now it is found that the prominent hot spot of this system was active during cycle 22. Another double-hot-spot system (with a period of 27.41 days) is found to be in operation in the northern hemisphere during solar cycles 19-21. Another interesting hot-spot system is a single hot spot with a rotation period of 27.0 days, which operated in the northern hemisphere during cycle 21. This hot spot may have the same cause as the 27.03 day periodicity observed in the solar wind speed and interplanetary magnetic field. During cycle 23, a double-hot-spot system with a rotation period of 28.2 days is detected in the southern hemisphere, but none are detected in the northern hemisphere.
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