In this paper, for an odd prime
p and
i=0,1, we investigate the cross-correlation between two decimated sequences,
s(2
t+
i) and
s(
dt), where
s(
t) is a
p-ary m-sequence of period
pn-1. Here we consider two cases of ${d}$, ${d=\frac{(p^m +1)^2}{2} }$ with ${n=2m}$, ${p^m \equiv 1 \pmod{4}}$ and ${d=\frac{(p^m +1)^2}{p^e + 1}}$ with
n=2
m and odd
m/
e. The value distribution of the cross-correlation function for each case is completely determined. Also, by using these decimated sequences, two new
p-ary sequence families of period ${\frac{p^n -1}{2}}$ with good correlation property are constructed.
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