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A method is proposed in this article to study the influence of discretization step on positivity for a certain class of fractional continuous discrete-time linear system introduced in Kaczorek (2011a, B. Pol. Acad. Sci-Tech. Sci. 59, 575—579). The relation between the value of the sampling step and positivity of this class of system is proposed, i.e. under which conditions the two-dimensional discrete-time linear system obtained by discretization from the two-dimensional continuous discrete-time linear system will be also positive if the two-dimensional continuous discrete-time linear system is positive. Numerical examples are introduced to illustrate the proposed results. [ABSTRACT FROM AUTHOR]