The present invention provides a method of obtaining an organism which has been characterized as having cells containing exogenous genetic material which includes any sequence of DNA that can be distinguished as exogenous by known molecular biological analysis by insertion of genetic material into an animal's genetic makeup. The insertion of the genetic material is done by inserting DNA that has been complexed with molecules that allow the DNA to be inserted into the chromosomes when injected into the cytoplasm, perivitelline space, or placed in surrounding culture media to be taken up and incorporated into the genome. When the DNA is complexed into the polyelectrolyte molecules by electrostatic attraction, the electric charge of DNA of the complex is partially to substantially neutralized. The present method does not require the genetic material to be introduced into the embryo at a particular stage in development.