In this paper, we take our theoretical point of departure in recent work in organisational economics on systems of human resource management (HRM) practices. We develop the argument that just as complementarities between new HRM practices influence financial performance positively, there are theoretical reasons for expecting them also to influence innovation performance positively. We examine this overall hypothesis by estimating an empirical model of innovation performance, using data from a Danish survey of 1,900 business firms. Using principal component analysis, we identify two HRM systems which are conducive to innovation. In the first one, seven of our nine HRM variables matter (almost) equally for the ability to innovate. The second system is dominated by firm‐internal and firm‐external training. Of the total of nine sectors that we consider, we find that the four manufacturing sectors correlate with the first system. Firms belonging to wholesale trade and to the ICT intensive service sectors tend to be associated with the second system.