We present a simple and robust method for brightness enhancement, efficiently transforming a radially polarized LG ${(0,1)}^{*}$ mode into a nearly Gaussian beam of much higher quality. We use for this a spatially variable retardation plate and a spatial filter. The analysis shows that the transformation yields an increase in brightness by a factor of 3.4. In the experiment, we transformed a high-power Nd:YAG radially polarized ${(0,1)}^{*}$ LG beam with power of $70\mathrm{W}$ and $M^2=2.6$ into a nearly Gaussian beam with $M^2=1.36$ . This resulted in brightness enhancement by a factor of 2.6.