  Let $A$ be a nonempty finite subset of an additive abelian group $G$. Define
$A + A := \{a + b : a, b \in A\}$ and $A \dotplus A := \{a + b : a, b \in
A~\text{and}~ a \neq b\}$. The set $A$ is called a {\em sum-dominant (SD) set}
if $|A + A| > |A - A|$, and it is called a {\em restricted sum-domonant (RSD)
set} if $|A \dotplus A| > |A - A|$. In this paper, we prove that for infinitely
many positive integers $k$, there are infinitely many RSD sets of integers of
cardinality $k$. We also provide an explicit construction of infinite sequence
of RSD sets.
