A method suitable for analysing the anomalous β-spectrum of RaE is developed. It is shown that, if the Gamow-Teller component of the β-decay interaction is of the tensor type, it is very difficult to explain the shape of the β-spectrum of RaE unless all of the following conditions are satisfied simultaneously: (a) the Fermi component is of the scalar type, (b) CS/CS′ = CT/CT′, and (c) CS/CT = real. Alternatively, if the Gamow-Teller component is of the axial vector type, the conditions are: (a) the Fermi component is of the vector type, (b) CV/C′V = CA/CA′, and (c) CV/CA = real.