This paper investigates $\alpha_i^{d}, i \in \{2, 3, 4\}$, selection principles (which are modification of known selection principles of Ko\v{c}inac) on a double sequence of double sequences of real numbers which converge to a point $a\in \mathbb{R}$ in Pringsheim's sense. A stronger result than one given in [6] will be proved for the $\alpha_2^{d}$ selection principle. Also, two more propositions will be proved for the $S_1^{d}$ and $S_1^{\varphi}$ selection principles, which are also improvements of results given in [6].