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We will give a characterization of stable real 
${{C}^{*}}$-algebras analogous to the one given for complex ${{C}^{*}}$-algebras by Hjelmborg and Rørdam. Using this result, we will prove that any real ${{C}^{*}}$-algebra satisfying the corona factorization property is stable if and only if its complexification is stable. Real ${{C}^{*}}$-algebras satisfying the corona factorization property include 
$\text{AF}$-algebras and purely infinite C*-algebras. We will also provide an example of a simple unstable C*-algebra, the complexification of which is stable.
