With the growing importance of intermediate goods, recent studies begin to suggest intermediate goods-skill complementarity and its potential effect on inequality. However, this possible complementarity has not yet been formally tested. This paper conducts a formal test on whether intermediate goods are complements for skilled labor. Using the panel data of 40 countries over the period 1995-2009, we estimate a two-level CES production function. Our results indicate that, at the aggregated one-sector level, the elasticity of substitution between intermediate goods and unskilled labor is significantly greater than that between intermediate goods and skilled labor. This confirms intermediate goods-skill complementarity. At the more disaggregated level, such complementarity is observed mainly in the heavy manufacturing industries and the service sector, whereas substitutability is confirmed in the primary sector and in light manufacturing industries. Moreover, intermediate goods-skill complementarity tends to be higher for industries whose shares of imported intermediate goods are higher.