The continuous process $X(t)=W_1(t)+\varphi(t)W_2(t)$, $0\leq t\leq1$, is considered, where $W_1(t)$ and $W_2(t)$ are independent Wiener processes and $\varphi(t)$ is a version of the Cantor distribution of function. The multiplicity of the non-Markovian process $X(t)$ is two. The proper canonical representation of $X(t)$ is also given.