It is usually believed that there is an order-disorder transition at 1090℃ in binary Ti-Ni alloys, as Honma et al. reported previously. The presence or absence of such transition is very important, because the result may greatly affect the martensitic transformation behavior,and the associated shape memory characteristics. In the present paper, we question whether such transition really exists or not. One of the difficulties in such experiments, including the work of Honma et al., lies in the fact that Ti can be easily oxidized at such high temperatures, which complicates the alloy behavior greatly and may lead to erroneous interpretation of experimental data. After doing carefully designed experiments on this point, we did not find any differential thermal analysis peak up to the melting temperature, or any drastic change in electrical resistance in a wide temperature region including 1090℃, which is the characteristic of order-disorder transition. These observations lead to the conclusion that such order-disorder transition does not exist in Ti-Ni binary shape memory alloys.