  We performed an experimental search for the bound state singlet deuteron
predicted in some microscopic calculations. The predicted energy of this
metastable level is in vicinity of the deuteron disintegration threshold. This
state should manifest itself in two-photon transition following thermal neutron
capture by protons. The experiment consists in the search for the second
gamma-ray in the cascade through a high statistics measurement of $\gamma$-ray
spectra after cold neutron capture by hydrogen nuclei. The upper limit $2\mu$b
(2$\sigma$ level) is obtained for the cross section of the singlet deuteron
production with the bound energy in the range 10-125 keV.
