Positions of leaves along a stem usually adhere to a genetically determined, species-specific pattern known as a leaf phyllotaxis. We investigated whether the arrangement of lateral secondary veins along primary midveins adhered to a species-specific pattern that resembled an alternate or opposite phyllotaxis. We analyzed the venation of temperate dicotyledonous species from different taxonomic groups and chose 18 woody and 12 herbaceous species that have reticulated leaf venation. The arrangement of the lateral veins was neither alternate nor opposite for any of the species. Lateral vein arrangements were instead mixtures of symmetric and asymmetric patterns. Our results show that lateral vein arrangements are related neither to stem-level leaf phyllotaxis (alternate vs. opposite) nor to life form (woody vs. herbaceous). Our results are therefore generally consistent with the canalization hypothesis that the locations of lateral veins are not completely specified genetically prior to leaf formation.