Let $p$ be a prime, $n=2m$ and $d=3p^{m}-2$ with $m\geq 2$ , and $\gcd (d,p^{n}-1)=1$ . In this paper, the correlation distribution between a $p$ -ary $m$ -sequence of period $p^{n}-1$ and its $d$ -decimation sequence is investigated in a unified approach. Some results for the binary case are extended to the general case. It is shown that the problem of determining the correlation distribution for $d$ can be reduced to that of solving two combinatorial problems related to the unit circle of the finite field $\mathbb {F}_{p^{n}}$ . For an arbitrary odd prime $p$ , it seems difficult to solve these two problems. However, for $p=3$ , by studying the weight distribution of the ternary Zetterberg code and counting the numbers of solutions of some equations over $\mathbb {F}_{3^{n}}$ , the two problems are solved, and thus, the corresponding correlation distribution for $d$ is completely determined. It is noteworthy that this is the first time that the correlation distribution for a non-binary Niho decimation has been determined since 1976.