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[en] The possibility of the growth of a small-scale dynamo in a random flow with a weak mirror asymmetry under subcritical generation conditions is investigated. We show that the appearance of an asymmetry in a flow with nonzero helicity leads to the generation of small-scale periodic perturbations. These perturbations, in turn, support active field generation on small scales. We describe the properties of this support, the generation rate, and the characteristic scales dependent on the velocity of the random flow and the degree of its helicity. Transferring the problem to the spectral domain, we demonstrate the formation of a two-component small- and large-scale spectrum that consists of a peak localized on large scales and power laws at large and small k. The possibility of directly checking the spectral properties being described in subcritical laboratory MHD conditions is specially noted.