Let
K
K
be a complete ultrametric algebraically closed field of characteristic zero, and let
M
(
K
)
{\mathcal {M}} (K)
be the field of meromorphic functions in
K
K
. For all set
S
S
in
K
K
and for all
f
∈
M
(
K
)
f\in {\mathcal {M}}(K)
we denote by
E
(
f
,
S
)
\displaystyle E(f,S)
the subset of
K
×
N
∗
K {\times } {\mathbb {N}}^{*}
:
⋃
a
∈
S
{
(
z
,
q
)
∈
K
×
N
∗
|
z
{\bigcup _{ a\in S}}\{(z,q)\in K {\times } \mathbb {N}^{*} \vert z
zero of order
q
of
f
(
z
)
−
a
}
.
q \text { of} f(z)-a\}.
After studying unique range sets for entire functions in
K
K
in a previous article, here we consider a similar problem for meromorphic functions by showing, in particular, that, for every
n
≥
5
n\geq 5
, there exist sets
S
S
of
n
n
elements in
K
K
such that, if
f
,
g
∈
M
(
K
)
f, g\in {\mathcal {M}} (K)
have the same poles (counting multiplicities), and satisfy
E
(
f
,
S
)
=
E
(
g
,
S
)
E(f,S)=E(g,S)
, then
f
=
g
f=g
. We show how to construct such sets.