The goals of this paper include the introduction of a new four-dimensional summability method construction by compounding a single four-dimensional method. The examination of this method begins with the characterization of its RH-regularity properties. In addition, the following inclusion and consistent theorems will be presented.

If $\{\alpha_m^\prime\}$, $\{\beta_n^\prime\}$, $\{\alpha_m\}$, and $\beta_n$ are sequences such that $\{\alpha_m\}$ and $\{\beta_n\}$ are monotone increasing with $\alpha_m^\prime\geq\alpha_m$ and $\beta_n^\prime\geq\beta_n$ for all sufficiently large $m$ and $n$ and if the transformations $B(\alpha_m^\prime, \beta_n^\prime)$ and $B(\alpha_m, \beta_n)$ are factorable and RH-regular then $B(\alpha_m^\prime, \beta_n^\prime)$ includes $B(\alpha_m, \beta_n)$.

The RH-regular matrix transformations of the form $B(r_m ,s_n)$ for which $r_1\leq r_2\leq r_3\leq\dots$ and $s_1\leq s_2\leq s_3\leq\dots$ constitute a double sequence of consistent family. Other implications and variations will also be presented.