In this paper, using componentwise treatment, the following theorems concerning the Boolean functions over the finite Boolean algebra $B$ are proved: extsc{Theorem 1.} The range of an isotone Boolean function $f\colon B^n\to B$ is the interval $[f(0,\dots,0),f(1,\dots,1)]$ and coincides with the set of all $a\in B$ such that $f(a,\dots,a)=a$. extsc{Theorem 2.} For every Boolean function $f\colon B^n\to B$, the function $(\ldots((f(x_1,\dots,x_n))^2_1)^2_2\ldots)^2_n$ is an isotone Boolean function, where \[ (g(x,\dots,x)^2_i=g(x_1,\dots,x_{i-1}, g(x_1,\dots,x_n),\dots,x_n). \] extsc{Theorem 3.} A Boolean function $f\colon B^n\to B$ is isotone if and only if $f(x_1,\dots,x_n)=(\dots((f(x_1,\dots,x_n))^2_1)^2_2\dots)^2_n$. The theorems are generalizations of results well known for Boolean functions of one variable.