We compute the tidal deformabilities for neutron star merger for equations of state with a strong first order phase transition producing a new separate branch in the mass-radius diagram. A case is found where all three possible pairs of combinations between these two neutron star branches are present for the total mass of $M=2.7M_odot$ of the observed merger event GW170817. It is demonstrated that the plot of the two tidal deformabilities $Lambda_1$ and $Lambda_2$ of the binary neutron star can show up to three separate branches. We propose that the future detections of neutron star merger events with the same value for $Lambda_1$ but different values of $Lambda_2$ serve as a signal for the existence of a strong first order phase transition in neutron star matter.
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