The possibility to verify the pseudo-Dirac nature of neutrinos is investigated here via the detection of ultra-high energy neutrinos from distant cosmological objects like 𝛾-ray bursts (GRBs). The very long baseline and the energy range from ∼TeV to ∼EeV for such neutrinos invoke the likelihood to probe very small pseudo-Dirac splittings. The expected secondary muons from such neutrinos that can be detected by a kilometer scale detector such as ICECUBE is calculated and compared with the same in the case of mass-flavour oscillations and for no oscillation cases. The calculated muon yields indicate that to probe such small pseudo-Dirac splittings one needs to look for a nearby GRB (red shift $z \sim 0:03$ or less) whereas for a distant GRB ($z \sim 1$) the flux will be much depleted and such phenomenon cannot be distinguished. Also calculated are the muon-to-shower ratios.