A measurement of the azimuthal asymmetry in dihadron production in deep-inelastic scattering of muons on transversely polarised proton (NH$_{3}$) targets are presented. They provide independent access to the transversity distribution functions through the measurement of the Collins asymmetry in single hadron production. The data were taken in the year $2010$ with the COMPASS spectrometer using a $160,mbox{GeV}/c$ muon beam of the CERN SPS, increasing by a factor of about three the available statistics of the previously published data taken in the year $2007$. The measured sizeable asymmetry is in good agreement with the published data. An approximate equality of the Collins asymmetry and the dihadron asymmetry is observed, suggesting a common physical mechanism in the underlying fragmentation.