All data available in B band for the BL Lac object Mkn 421 from 22 publications are used to construct a historical light curve, dating back to 1900. It is found that the light curve is very complicated and consists of a set of outbursts with very large duration. The brightness of Mkn 421 varies from 11.6 magnitude to more than 16 magnitude. Analyses with Jurkevich method of computing periods of cyclic phenomena reveal in the light curve two kinds of behaviors. The first one is non-periodic with rapid, violent variations in intensity on time scales of hours to days. The second one is periodic with a possible period of 23.1 +/- 1.1 years. Another possible period of 15.3 +/- 0.7 years is not very significant. We have tested the robustness of the Jurkevich method. The period of about one year found in the light curves of Mkn 421 and of other objects is a spurious period due to the method and the observing window. We try to explain the period of 23.1 +/- 1.1 years under the thermal instability of a slim accretion disk around a massive black hole of mass 2 10(6) M..
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