This paper presents an analysis of nonlinear interaction between extraordinary waves propagating perpendicular to the static magnetic field in a cold homogeneous magnetoplasma. It is first shown that the synchronism conditions for wave/wave interaction can be met over wide ranges of parameters. A theory of the interaction based on cold plasma theory is then described which yields a closed‐form solution for signal growth by the mechanism of parametric amplification. Numerical solutions are presented for the growth rate, and associated frequencies and wavenumbers, over a range of magnetoplasma parameters. The relevance of these results to laboratory and space plasma experimentation, and to verification of the theory, is discussed.