Abstract We have recently reported on an indication of the strange tribaryon state, S+, with a mass M ∼ 3140 MeV / c 2 and width Γ 23 MeV / c 2 , in the neutron time-of-flight (TOF) spectrum of the He 4 ( K stop − , n π ± ) reaction of the KEK-PS E471 experiment in a search for the deeply bound narrow K − p p n (total isospin T = 0 ) state. In an attempt to confirm the state and search for other possible T = 0 , 1 tribaryonic states, we have re-measured the neutron energy spectrum of the same reaction in the KEK-PS E549 experiment with an upgraded setup for which the TOF resolution was improved 1.5 times and the statistics was increased 6 times. However, in the neutron spectra, we find such a smooth distribution that we conclude the state is either not so strong to stick out of the inclusive background or too broad to be identified as a distinct peak. We estimated the upper limits of the formation probability of the possible tribaryonic state for three widths, 0, 20, and 40 MeV / c 2 . The obtained upper limit (95% CL) for a state as narrow as 20 MeV / c 2 is at most 1% per stopped kaon over the wide mass range of 3000–3200 MeV/c2, while it reaches to 4 ∼ 5 % at around 3140 MeV/c2 for Γ ⩾ 40 MeV / c 2 , implying the possible existence of unknown processes including tribaryonic formation.