If ${eta};>;1$, then every non-negative number x has a ${eta}-expansion$, i.e., $$x;=;{epsilon}_0(x);+;{frac{epsilon_1(x)}{eta}};+;{frac{epsilon_2(x)}{eta}};+;{cdots}$$ where ${epsilon}_0(x);=;[x],;{epsilon}_1(x);=;[eta(x)],;{epsilon}_2(x);=;[eta(({eta}x))]$, and so on ([x] denotes the integral part and (x) the fractional part of the real number x). Let T be a transformation on [0,1) defined by $x;{ ightarrow};({eta}x)$. It is well known that the relative frequency of $k;{in};{0,;1,;{cdots},;[eta]}$ in ${eta}-expansion$ of x is described by the T-invariant absolutely continuous measure ${mu}_{eta}$. In this paper, we show the mod M normality of the sequence ${{in}_n(x)}$.