For an analytic function f on the unit disk D = {z : |z| < 1} satisfying f (0) = 0 = f ′(0) − 1, we obtain sufficient conditions so that f satisfies |(z f ′(z)/ f (z))2 − 1| < 1. The technique of differential subordination of first and second order is used. The admissibility conditions for lemniscate of Bernoulli are derived and employed in order to prove the main results