  COMPASS is a fixed-target high energy physics experiment at the SPS at CERN
\cite{Abbon:2007pq}. One of the important objectives of the experiment is the
exploration of the transverse spin structure of the nucleon via spin dependent
azimuthal asymmetries in single-hadron production in deep inelastic scattering
of polarized leptons off transversely polarized target. For this purpose a
series of measurements were made in COMPASS, using 160 GeV/c longitudinally
polarized muon beam and transversely polarized $^6LiD$ (in 2002, 2003 and 2004)
and $NH_3$ (in 2007 and 2010) targets.
  Till now main attention was focused on Collins and Sivers asymmetries and
obtained results play an important role in the general understanding of the
three-dimensional nature of the nucleon in terms of Transverse Momentum
Dependent (TMD) Parton Distribution Functions (PDFs) and Fragmentation
Functions (FFs).
  In addition to these two measured leading-twist effects, the SIDIS
cross-section counts six more target transverse spin dependent azimuthal
effects, which have their own well defined leading or higher-twist
interpretation in terms of QCD parton model. So far COMPASS presented
preliminary results for these asymmetries from deuteron
\cite{Parsamyan:2007ju},\cite{Kotzinian:2007uv} and "proton-2007" data
\cite{Parsamyan:2010se}. In this contribution we review the results obtained
with the last "proton-2010" data sample.
