Abstract We present a new algorithm to perform blind signal separation (BSS), which takes a trade-off between the ordinary gradient infomax algorithm and the natural gradient infomax algorithm. Analyzing the algorithm, we show that desired equilibrium points are locally stable by choosing appropriate score functions and step sizes. The algorithm provides better performance than the ordinary gradient algorithm, and it is free from approximation error and the small-step-size restriction of the natural gradient algorithm. In simulations on convolved mixtures, the algorithm provides much better performance than the other algorithms while requiring less computation.