Let $X$ be a set, and let $\hat{X} = \bigcup^\infty_{n = 0} X_n$ be the superstructure of $X$, where $X_0 = X$ and $X_{n + 1} = X_n \cup \mathscr{P}(X_n) (\mathscr{P}(X)$ is the power set of $X$) for $n \in \omega$. The set $X$ is called a flat set if and only if $X \neq \varnothing.\varnothing \not\in X.x \cap \hat X = \varnothing$ for each $x \in X$, and $x \cap \hat{y} = \varnothing$ for $x.y \in X$ such that $x \neq y$, where $\hat{y} = \bigcup^\infty_{n = 0} y_n$ is the superstructure of $y$. In this article, it is shown that there exists a bijection of any nonempty set onto a flat set. Also, if $\tilde W$ is an ultrapower of $\hat X$ (generated by any infinite set $I$ and any nonprincipal ultrafilter on $I$), it is shown that $\tilde W$ is a nonstandard model of $X$: i.e., the Transfer Principle holds for $\hat X$ and $\tilde W$, if $X$ is a flat set. Indeed, it is obvious that $\tilde W$ is not a nonstandard model of $X$ when $X$ is an infinite ordinal number. The construction of flat sets only requires the ZF axioms of set theory. Therefore, the assumption that $X$ is a set of individuals (i.e., $x \neq \varnothing$ and $a \in x$ does not hold for $x \in X$ and for any element $a$) is not needed for $\tilde W$ to be a nonstandard model of $X$.