A novel maize variety designated 36H43 and seed, plants and plant parts thereof, produced by crossing Pioneer Hi-Bred International, Inc. proprietary inbred maize varieties. Methods for producing a maize plant that comprises crossing maize variety 36H43 with another maize plant. Methods for producing a maize plant containing in its genetic material one or more traits introgressed into 36H43 through backcross conversion and/or transformation, and to the maize seed, plant and plant part produced thereby. This invention relates to the maize variety 36H43, the seed, the plant produced from the seed, and variants, mutants, and minor modifications of maize variety 36H43. This invention further relates to methods for producing maize varieties derived from maize variety 36H43 and to the maize varieties derived by the use of those methods.