Ten new 0–4, 1–0, 1–1, 3–3, 3–5, 3–6, 3–7, 4–6, 4–7, and 5–8 bands of the first-negative (B 2 Σ + →X 2 Σ + ) system of 13C16O+ were observed and their rotational structure was analyzed for the first time. These bands were recorded by means of classical spectrographical methods under high resolution. This allowed one to observe a spin splitting in most lines of the recorded bands. The effective Hamiltonian of Brown with the matrix elements for the 2Σ+ states taken from a work by Amiot et al. [J. Mol. Spectrosc. 87 (1981) 196–218] has been used to obtain the rovibronic structure parameters of the individual bands from the observed wavenumbers of lines. The molecular constants obtained in this way were then merged with those derived by us earlier. For this purpose the least-squares merge procedure was used. This made it possible to obtain a wide set of precise constants of the rotational structure in 15 vibrational levels, for the X2Σ+(v=0–8) ground state and for the second B 2 Σ + (v=0–5) excited state in 13C16O+. On the basis of these final constants it was possible to calculate the equilibrium molecular constants, and the RKR potential curves for the X 2 Σ + and B 2 Σ + electronic states as well as Franck–Condon factors and r-centroids for the first-negative bands in 13C16O+.