  Let G be a finite abelian group of order n. For a complex valued function f
on G, let \fht denote the Fourier transform of f. The uncertainty inequality
asserts that if f \neq 0 then |supp(f)| |supp(\fht)| \geq n. Answering a
question of Terence Tao, the following improvement of the classical inequality
is shown: Let d_1<d_2 be two consecutive divisors of n. If d_1 \leq k=|supp(f)|
\leq d_2 then: |supp(\fht)| \geq \frac{n(d_1+d_2-k)}{d_1 d_2}
