We demonstrate an efficient transformation of a linearly polarized Gaussian beam to a radially or an azimuthally polarized doughnut (0,1)* Laguerre-Gaussian beam of high purity. We use a spatially variable retardation plate, composed of eight sectors of a λ/2 retardation plate, to transform a linear polarization distribution to radial/azimuthal distribution. We transformed an Nd:YAG Gaussian beam with M2=1.3 to a radially and azimuthally polarized (0,1)* Laguerre-Gaussian beams with M2=2.5 and degree of radial/azimuthal polarization of 96-98%.