The paper introduces MC+, a fast, continuous, nearly unbiased, and accurate method for penalized variable selection in high-dimensional linear regression. MC+ combines a minimax concave penalty (MCP) and a penalized linear unbiased selection (PLUS) algorithm. The MCP ensures convexity in sparse regions, while PLUS computes multiple exact local minimizers of the penalized loss function. The method is shown to have high probability of correctly selecting variables without assuming strong conditions, and it achieves minimax convergence rates for estimating regression coefficients in $\ell_r$ balls. The paper also discusses the continuity of estimators, unbiased estimation of risk, and noise level estimation, providing a comprehensive framework for penalized variable selection. Simulation results demonstrate the superior performance of MC+ in terms of selection accuracy and computational efficiency compared to other methods like LASSO and SCAD.The paper introduces MC+, a fast, continuous, nearly unbiased, and accurate method for penalized variable selection in high-dimensional linear regression. MC+ combines a minimax concave penalty (MCP) and a penalized linear unbiased selection (PLUS) algorithm. The MCP ensures convexity in sparse regions, while PLUS computes multiple exact local minimizers of the penalized loss function. The method is shown to have high probability of correctly selecting variables without assuming strong conditions, and it achieves minimax convergence rates for estimating regression coefficients in $\ell_r$ balls. The paper also discusses the continuity of estimators, unbiased estimation of risk, and noise level estimation, providing a comprehensive framework for penalized variable selection. Simulation results demonstrate the superior performance of MC+ in terms of selection accuracy and computational efficiency compared to other methods like LASSO and SCAD.