During the past years, there has been an increasing interest in the construction of alternative basis sets for electronic systems. .In this work, by the use of generalized exponential functions approach, new efficient exponential type basis sets which include the B functions in the radial part have been constructed. Additional variational flexibility for the radial part of B functions is obtained by replacing the radial variable by r(mu), with mu optimisable. Thus, the new variational parameter mu in generalized B functions greatly improves the quality of atomic orbitals in the LCAO calculations. Results obtained using generalized B function basis sets within the minimal basis framework are compared to the results of the standard B functions basis sets and numerical Hartree-Fock values for atomic systems.