A hereditarily decomposable, irreducible, metric continuum
M
M
admits a mapping
f
f
onto
[
0
,
1
]
[0,1]
such that each
f
−
1
(
t
)
{f^{ - 1}}(t)
is a nowhere dense subcontinuum. The sets
f
−
1
(
t
)
{f^{ - 1}}(t)
are the tranches of
M
M
and
f
−
1
(
t
)
{f^{ - 1}}(t)
is a tranche of cohesion if
t
∈
{
0
,
1
}
t \in \{ 0,1\}
or
f
−
1
(
t
)
=
C1
(
f
−
1
(
[
0
,
t
)
)
)
∩
C1
(
f
−
1
(
(
t
,
1
]
)
)
{f^{ - 1}}(t) = {\text {C1}}({f^{ - 1}}([0,t))) \cap {\text {C1}}\,({f^{ - 1}}((t,1]))
. The following answer a question of Mahavier and of E. S. Thomas, Jr. Theorem. Every hereditarily decomposable continuum contains a subcontinuum with a degenerate tranche. Corollary. If in an irreducible hereditarily decomposable continuum each tranche is nondegenerate then some tranche is not a tranche of cohesion. The theorem answers a question of Nadler concerning arcwise accessibility in hyperspaces.