The calculation of cross-correlation between a sequence with good autocorrelation and its decimated sequence is an interesting problem in the field of sequence design. In this letter, we consider a class of ternary sequences with perfect autocorrelation, proposed by Shedd and Sarwate (IEEE Trans. Inf. Theory, 1979, DOI: 10.1109/TIT.1979.1055998), which is generated based on the cross-correlation between m-sequence and its d-decimation sequence. We calculate the cross-correlation distribution between a certain pair of such ternary perfect sequences and show that the cross-correlation takes three different values.