  In the present article we introduce and study a novel type of solutions of
the general Heun's equation. Our approach is based on the symmetric form of the
Heun's differential equation yielded by development of the Felix Klein
symmetric form of the Fuchsian equations with an arbitrary number $N\geq 4$ of
regular singular points. We derive the symmetry group of these equations which
turns to be a proper extension of the Mobius group. We also introduce and study
new series solution of symmetric form of the general Heun's differential
equation (N=4) which treats simultaneously and on an equal footing all singular
points. Hopefully, this new form will simplify the resolution of the existing
open problems in the theory of general Heun's functions and can be used for
development of new effective computational methods.
