The present invention relates to an improved method for producing a transgenic plant of the genus Triticum, with steps of a) Rhizobiaceae-mediated transforming of at least one cell of a plant of the genus Triticum with a genetic component, and b) regenerating of a transgenic plant of the genus Triticum from a transformed cell, where from step (a) to step (b) there is no selecting of a transformed cell based on a trait mediated by the genetic component, or of a part thereof.