A meromorphic functionfdefined in the unit discDof a complex plane, is called a normal function ifwhereis the spherical derivativeoff. Further, we say thatfis a little normal function ifWe answer two open questions raised by R. Aulaskari and R. Zhao (Complex Variables Vol. 28, 1995, pp. 135-148) on normal functions and little normal functions in negative and give a new characterization of normal functions.