We prove that $M_1longrightarrow^f;M_2$ is an injective representation of a quiver $Q={ullet}{ ightarrow}{ullet}$ if and only if $M_1;and;M_2$ are injective left R-modules, $M_1longrightarrow^f;M_2$ is isomorphic to a direct sum of representation of the types $E_l{ ightarrow}0$ and $M_1longrightarrow^{id};M_2$ where $E_l;and;E_2$ are injective left R-modules. Then, we generalize the result so that a representation$M_1longrightarrow^{f_1};M_2; longrightarrow^{f_2};cdots;longrightarrow^{f_{n-1}};M_n$ of a quiver $Q={ullet}{ ightarrow}{ullet}{ ightarrow}{cdots}{ ightarrow}{ullet}$ is an injective representation if and only if each $M_i$ is an injective left R-module and the representation is a direct sum of injective representations.