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Chemical Langevin Equation (CLE) describes a useful approximation in stochastic modeling of chemical reactions. CLE-based τ-leaping algorithm updates the quantities of every molecule in a reaction system with a period of τ, firing every reaction in the system so many times that the concentration of each molecule can be assumed to remain in the current concentration state. Substituting the Brownian motion in the CLE with a Levy flight, one might expect the CLE to converge more rapidly. This work shows that alpha (Levy)-stable increments can be used in τ-leaping, demonstrating it with the example of a detailed kinetic model describing the enzymatic transgalactosylation reaction during lactulose hydrolysis.