Recently (2015) at the Institute of Physics of the Jagiellonian University, a commercial electron beam ion source (Dresden EBIT, DREEBIT Co.) was installed for teaching and scientific purposes. The first experiments were focused on observation of radiative recombination and dielectronic recombination (DR). A good resolution of the X‐ray spectra for DR in argon encouraged a more detailed search. An investigation of higher order resonances, namely, trielectronic recombination (TR: KK‐LLL, KK‐LLM,…) in argon ions, was initiated. The present experiment was conducted while scanning the electron beam energy of the EBIT over the region 5,700–7200 eV. This electron energy region was expected to manifest an enhancement of the Ar‐K X‐ray emission due to TR processes mentioned above. Indeed, a maximum‐like behavior of the radiation intensity was observed.