Context. Binary systems with similar components are ideal laboratories that allow several physical processes to be tested, such as the possible chemical pattern imprinted by the planet formation process. Aims. We explore the probable chemical signature of planet formation in the remarkable binary system HD 80606−HD 80607. The star HD 80606 hosts a giant planet with ∼4 M Jup detected by both transit and radial velocity techniques, which is one of the most eccentric planets detected to date. We study condensation temperature T c trends of volatile and refractory element abundances to determine whether there is a depletion of refractories, which could be related to the terrestrial planet formation. Methods. We carried out a high-precision abundance determination in both components of the binary system via a line-by-line, strictly differential approach. First, we used the Sun as a reference and then we used HD 80606. The stellar parameters T eff , log g, (2009, A&A, 497, 563). The T c trends were also compared mutually between both stars of the binary system. Results. From the study of T c trends, we concluded that the stars HD 80606 and HD 80607 do not seem to be depleted in refractory elements, which is different for the case of the Sun. Then, following the interpretation of Meléndez et al. (2009), the terrestrial planet formation would have been less efficient in the components of this binary system than in the Sun. The lack of a trend in refractory elements with T c between both stars implies that the presence of a giant planet do not neccesarily imprint a chemical signature in their host stars, similar to the recent result of Liu et al. (2014, MNRAS, 442, L51). This is also in agreement with Meléndez et al. (2009), who suggest that the presence of close-in giant planets might prevent the formation of terrestrial planets. Finally, we speculate about a possible, ejected or non-detected, planet around the star HD 80607.