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We discuss the importance of $Z_2$ symmetry of large $N=4$ superconformalalgebra for finding its free field realization that is more complete than themost commonly used one, that is, the Sevrin, Troost and van Proeyenrealization. This in turn has implications for the search of a conformal fieldtheory dual to superstrings moving in $AdS_3 \times S^3 \times S^3 \times S^1$background.

$Z_2$ Symmetry of $AdS_3 \times S^3 \times S^3 \times S^1$ Superstrings