We have performed a careful measurement of the shape of the beta spectrum of He⁶. A detailed study of the phenomenon of electron scattering in our thin lens magnetic spectrometer enabled us to interpret the spectrum shape from the end point at Wₒ = 3.50 ± .02 Mev. down to 1/14 Wₒ = 0.250 Mev. The experimental shape has been compared with the theoretically predicted shape for allowed spectra. The influence of the pseudoscalar interaction on the shape of the He⁶ spectrum has also been considered. From these measurements we have been able to set limits on the Fierz interference in the Gamow-Teller interaction as well as on the magnitude of the pseudoscalar coupling constants. These limits have been interpreted in terms of the relative magnitudes of the axial vector, pseudoscalar, and tensor coupling constants using the two component theory of the neutrino and assuming that the complete beta decay Hamiltonian proposed by Lee and Yang is or is not invariant under time reversal. We have also calculated the effect on the spectrum shape of the production of inner Bremsstrahlung in beta decay and have shown this effect to be at the limit of experimental detectability.