In this work, we propose a segment-based representation for the upper bound of the non-dominated set in interval branch & bound solvers for biobjective non linear optimization. We ensure that every point over the upper line segments is dominated by at least one point in the feasible objective region. Segments are generated by linear envelopes of the image of feasible line segments. Finally, we show that the segment-based representation together with methods for generating upper line segments allows us to converge more quickly to the desired precision of the whole strategy. The code of our solver can be found in our git repository (https://github.com/INFPUCV/ibex-lib/tree/master/plugins/optim-mop).