We describe the equations of the Rees algebra
R
(
I
)
\mathbf {R}(I)
of an equimultiple ideal
I
I
of deviation one provided that
I
I
has a reduction generated by a regular sequence
x
1
,
…
,
x
s
x_1,\ldots ,x_s
such that the initial forms
x
1
∗
,
…
,
x
s
−
1
∗
x_1^*,\ldots ,x_{s-1}^*
are a regular sequence in the associated graded ring. In particular, we prove that there is a single equation of maximum degree in a minimal generating set of the equations of
R
(
I
)
\mathbf {R}(I)
, which recovers some previous known results.