An improvement on the total energy results reported in Ref. 9 in atomic calculations based on a modified type hyperbolic cosine function cosh(beta(mu) + gamma) is presented. It is shown that the noninteger n-generalized exponential type orbitals r(n*-1)e(-zeta r mu) with modified type hyperbolic cosine as radial basis functions are a much better approximation to the Hartree-Fock orbitals than a double-zeta basis set of Slater type functions. The efficiency of the new basis function is tested by application to some closed and open shell neutral atoms and their ions. A substantial improvement in both the total and orbital energies is obtained within the minimal basis sets framework. The total energy values obtained in this work are significantly close to the numerical Hartree-Fock results. These results supersede all previous minimal basis function total energies achieved in the literature.