In general, eight target transverse spin-dependent azimuthal modulations are allowed in semi inclusive deep inelastic scattering of polarized leptons on a transversely polarized target. In the QCD parton model four of these asymmetries can be interpreted within the leading order approach. Two of them, namely Collins and Sivers effects were already measured by HERMES and COMPASS experiments. Other two leading twist and remaining four azimuthal asymmetries which can be interpreted as twist-three contributions have been measured for the first time in COMPASS using a 160 GeV/c longitudinally polarized ($P_{beam}simeq -0.8$) muon beam and a transversely polarized $^6LiD$ target. We present here the preliminary results from the 2002-2004 data.
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