[en] Complete text of publication follows. In the present paper supernarrow dibaryons, a decay of which into two nucleons is forbidden by the Pauli exclusion principle are considered (1,2). If this state mass is limited by 2m_N + m_π (m_N(m_π) is the nucleon (pion) mass) above the decay of it must be accompanied mainly by emitting a photon. This leads to a small width ≤ 1keV of such NN-decoupled supernarrow dibaryon (SND). There are only two experimental works (3,4) where such state was studied. The results of these works disagrees each to other. However, in some cases the events of the SND production can be identified by using the kinematics restrictions without the photon registration. As will be shown below, the nucleons and the deuteron from the decay of the dibaryons under consideration into γNN and γd have to be emitted in a narrow angular cone with respect to the direction of motion of the dibaryon. The size of this cone depends also on the quantum numbers of the dibaryon. So, a detection of the proton spectator in coincidence with the proton (or the deuteron) from the dibaryon decay at correlated angles gives a good possibility to separate the SNDs from the background and to determine their quantum numbers. Our earlier experiments were described in anywhere (5). In the present paper we give a further study of the reactions pd → p + pX₁ and pd → p + dX₂ (where X₁ and X₂ are undetected particles in this experiment) with the aim to search for SNDs at the Linear proton accelerator using an improved facility. We will consider the following dibaryons: D(T = 0, J^P = 0⁺) D(0, 0^-), D(1, 1⁺) and D(1, 1^-). We insist on the narrow peaks in missing mass spectra which have been observed (as in earlier experiments) at 1905 and 1924 MeV with the statistical significance more than 4.5 S.D. From the comparison between the obtained data and the theoretical predictions the peak found at 1905 MeV most likely is explained by a supernarrow dibaryon with the isotopic spin equal to 1. The peak at 1924 MeV is most likely a supernarrow dibaryon also. (author)