We propose a novel hybrid algorithm“Brent-STEP” for uni- variate global function minimization, based on the global line search method STEP and accelerated by Brent’s method, a local optimizer that combines quadratic interpolation and golden section steps. We analyze the performance of the hy- brid algorithm on various one-dimensional functions and ex- perimentally demonstrate a significant improvement relative to its constituent algorithms in most cases. We then gener- alize the algorithm to multivariate functions, adopting the recently proposed  scheme to interleave evaluations across dimensions to achieve smoother and more efficient conver- gence. We experimentally demonstrate the highly competi- tive performance of the proposed multivariate algorithm on separable functions of the BBOB benchmark. The combina- tion of good performance and smooth convergence on sepa- rable functions makes the algorithm an interesting candidate for inclusion in algorithmic portfolios or hybrid algorithms that aim to provide good performance on a wide range of problems.