The purpose of this note is to give a more refined version of a theorem of Efroymson: If
U
⊂
R
n
U \subset {{\mathbf {R}}^n}
is defined by polynomial inequalities of the form
f
i
>
0
,
i
=
1
,
…
,
p
{f_i} > 0,i = 1, \ldots ,p
, and if g is a positive definite Nash function on U, then g is a finite sum of squares of Nash meromorphe functions on U.