Radially-polarized beams can be strongly amplified without significant birefringence- induced aberrations. However, further improvement of the beam quality is desirable. In effort to transform the radially-polarized beam to a nearly-Gaussian beam, we consider effect of a spiral phase element (SPE) on the Laguerre-Gaussian (LG) (0,1)* beam with radial polarization, and compare this with the case when the input beam is a LG (0,1)* beam with spiral phase and uniform or undefined polarization. The LG (0,1)* beam with radial polarization, despite its identity in intensity profile to the beam with spiral phase, has distinctly different properties when interacting with the SPE. With the SPE and spatial filter, we transformed the radially-polarized (0,1)* mode with M2=2.8 to a nearly-Gaussian beam with M2=1.7. Measured transformation efficiency was 50%, and the beam brightness P/(M2)2 was practically unchanged. The SPE affects polarization state of the radially-polarized beam, leading to appearance of spin angular momentum in the beam center at the far-field.