Background: β-delayed multiple neutron emission has been observed for some nuclei with A≤100, being the Rb100 the heaviest β2n emitter measured to date. So far, only 25P2n values have been determined for the ≈300 nuclei that may decay in this way. Accordingly, it is of interest to measure P2n values for the other possible multiple neutron emitters throughout the chart of the nuclides. It is of particular interest to make such a measurement for nuclei with A>100 to test the predictions of theoretical models and simulation tools for the decays of heavy nuclei in the region of very neutron-rich nuclei. In addition, the decay properties of these nuclei are fundamental for the understanding of astrophysical nucleosynthesis processes, such as the r-process, and safety inputs for nuclear reactors. Purpose: To determine for the first time the two-neutron branching ratio, the P2n value, for Sb136 through a direct neutron measurement and to provide precise P1n values for Sb136 and Te136. Method: A pure beam of each isotope of interest was provided by the JYFLTRAP Penning trap at the Ion Guide Isotope Separator On-Line (IGISOL) facility of the University of Jyväskylä, Finland. The purified ions were implanted into a moving tape at the end of the beam line. The detection setup consisted of a plastic scintillator placed right behind the implantation point after the tape to register the β decays and the BELEN detector, based on neutron counters embedded in a polyethylene matrix. The analysis was based on the study of the β- and neutron-growth-and-decay curves and the β-one-neutron and β-two-neutron time correlations, which allowed us the determination of the neutron-branching ratios. Results: The P2n value of Sb136 was found to be 0.14(3)% and the measured P1n values for Sb136 and Te136 were found to be 32.2(15)% and 1.47(6)%, respectively. Conclusions: The measured P2n value is a factor 44 smaller than predicted by the finite-range droplet model plus the quasiparticle random-phase approximation (FRDM+QRPA) model used for r-process calculations.