  Wave functions of a new functional kind have been proposed for Helium-like
atoms in this work . These functions explicitly depend on interelectronic and
hyperspherical coordinates. The best ground state energy for the Helium atom $
-2.903724376677 a.u.$ has been calculated with variational method with basis
set of simple functions with a single exponential parameter. To the author's
knowledge, this is the best result with use of hyperspherical coordinates so
far. Comparable result has been obtained for the hydrogen anion. For Helium
atom, our best wave functions matched the Kato cusp conditions within the
accuracy below $6.10^{-4} $. An important feature of proposed wave functions is
the inclusion of negative powers of $R=\sqrt(r^{2}_{1}+r^{2}_{2})$ in
combination with positive powers of $r_{12}$ into the wave function. We showed
that this is necessary condition for proposed wave function to be a formal
solution of Schr\"odinger equation.
