Let
H
2
(
S
)
H^{2}(S)
be the Hardy space on the unit sphere
S
S
in
C
n
\mathbf {C}^{n}
. We show that a set of inner functions
Λ
\Lambda
is sufficient for the purpose of determining which
A
∈
B
(
H
2
(
S
)
)
A\in {\mathcal {B}}(H^{2}(S))
is a Toeplitz operator if and only if the multiplication operators
{
M
u
:
u
∈
Λ
}
\{M_{u} : u \in \Lambda \}
on
L
2
(
S
,
d
σ
)
L^{2}(S,d\sigma )
generate the von Neumann algebra
{
M
f
:
f
∈
L
∞
(
S
,
d
σ
)
}
\{M_{f} : f \in L^{\infty }(S,d\sigma )\}
.