In this work we propose a segment-based representation for the upper bound of the non-dominated set in interval branch & bound solvers for bi-objective non linear optimization. We also warranty that every point over the upper segments is dominated by at least one point in the feasible objective region. Segments are generated by linear envelopes of the image offeasible line-segments. The segment-based representation allows us to converge more quickly to the desired precision of the whole strategy.