Exclusive diffractive Higgs boson production is an interesting process which could be studied at the Large Hadron Collider. While the cross section for the Higgs boson production at the Fermilab Tevatron Collider is too low for this channel, it is important to check if the class of exclusive diffraction events exists. We present the evidence for the high mass exclusive dijet production in the D0 experiment. Hard diffractive processes are usually described by the exchange of a colorless object called Pomeron. In diffractive hadron hadron collisions, the hadrons will exchange the Pomeron and either one or both hadrons will not dissolve. The events are identified by either a presence of a large forward region of the detector devoid of any activity (rapidity gap) or by a tagging of the intact beam hadron(s). A subset of diffractive events is called exclusive when the whole Pomeron energy is used to produce the diffractive state, i.e there are no Pomeron remnants. Exclusive diffractive production (EDP) of the Higgs boson or any other new final state X pp --> p + X + p has been recently proposed as a search channel at the LHC. The cross section for the Higgs boson production is too low at the Tevatron (0.2fb is predicted for a Higgs boson mass of 120 GeV), but it is important to check if this class of events exists in this kinematic region. The CDF Collaboration has recently confirmed the existence of EDP in several channels. In this report, we present the evidence for the exclusive production of high dijet invariant mass events, i.e. a dijet event accompanied by large rapidity gaps on both sides of the calorimeter.