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We show that the large variations in the X-ray flux of the extreme narrow-line Seyfert 1 galaxy IRAS 13224– 3809, measured during a 10 day ASCA observation, have a two-parameter lognormal distribution of multiplicative standard deviation σmult = 2.7 and that the amplitude of variability at any given moment is proportional to the flux level. We find similar behavior in earlier ROSAT soft X-ray monitoring. There is no evidence of a nonvariable component. The flux-dependent behavior of the variability rules out linear shot-noise models. Although at first glance the variations of the ASCAlight curve for IRAS 13224–3809 appear to exhibit nonstationary behavior with quiescent low states and more active flaring high states, our results show that the multiplicative variance is constant. Monte Carlo simulations of constant σmult give excellent matches to the observed X-ray light curve without the need to invoke special low and high states. This supports a picture in which the long-term variability is fundamental both in active galactic nuclei and in X-ray binaries. The lognormal flux distribution and the constancy of σmult are incompatible with the power-law distribution of flaring amplitudes expected from self-organized critical behavior. We discuss mechanisms that can generate lognormal flux distributions.