Effect of aging at 873 K on the two-step B2→B19→B19′ transformation of a shape memory Ti–40.5Ni–10Cu alloy was studied. It was found that the start temperature of the B2→B19 transformation and that of the B19→B19′ transformation increase with increasing aging time. The start temperatures of the reverse transformations also increase. The temperature range of the two-step transformation decreases with increasing aging time. The aged Ti–40.5Ni–10Cu alloy is composed of the matrix with B2-type structure (a_c=0.3029 nm) and precipitates with C11_b-type structure (a_t=0.3132 nm, c_t=0.7991 nm). The precipitates are partly coherent with the matrix and are plate-like in shape having a orientation relationship [100]_c//[100]_t and [001]_c//[001]_t, and a habit plane {001}_c. The increase of transformation temperature is caused by the precipitation through aging. The precipitation increases the Ti content of the matrix, and the precipitates act as a nucleation sites of B19 martensite due to strain field around them preferable for the B19 martensite.