We examine the relative strength of Fe II λ4570 in 138 active galactic nuclei in relation to the line width of Hβ. For objects with FWHM (Hβ) greater than 6000 km s^-1^, the mean Fe II λ4570/Hβ intensity ratio is 0.21, less than half of that in the other objects. The result confirms a general tendency, seen in earlier work on smaller samples, that strong optical Fe II emission is not found in objects showing very broad emission lines. In particular, all five objects with exceptionally broad and flat profiles, such as Arp 102B, have weak or absent Fe II emission. We have verified that this effect is not an artifact of blending of the Fe II multiplets or of underestimation of the Hβ line width due to blending with Fe II features. The anticorrelation between the Fe II λ4570 strength and line width may be interpreted as an effect of source orientation. The Fe II region is either highly anisotropic or is not coextensive with the conventional broad-line region such as the assumed disk-shaped low- ionization zone. This is consistent with the Fe II region being associated with a small-scale jet and embedded in a thick torus, and hence being visible only in nearly face-on positions.