Abstract: The events of which geomagnetic indices C9s are all larger than L (L is a constant) are noticed. The number of times of the events in a year is taken to express the level of geomagnetic disturbance of the year. Six cases are studied:L=3, 4 and 5; each of them is subdivided into two subcases: recurrent events and general events.The method of the curve fitting with piecewise polynomials is used to derive an averaged experimental relationship f(R) between the number of times in a year C_k and the sunspot relative number R_k (k is the order of the years from 1980 to 1979). Then, △_k = C_k - f_k (f_k = f(R_k)) are calculated. The result shows that: 1, for the 'solar cycles', each of which begins at he year four years before the minimum of the cor responding solar cycle, the signs of the average values of △_k alternate, ('sign alternating' fule +,-,+,-,......); 2. the 'sign alternating' rule oceurs in all the six subcases. It is mostly likely that the rule is caused by thereversal of the solar polar fields. After a further dividing of the 'cycles', every cycle has own dispersity (o) about its averaged △, △. The sequence of a shows a long term period of about 70 years.