It is possible for there to be a completely systematic relationship between the two variables but still no

There is a systematic relationship between the two variables, but the relationship is not linear since a straight line cannot come close to going through the points.

Pearson's Product Moment Correlation is the most commonly- used index of the degree of linear relationship. Spearman's rho is another commonly-used measure. Both of these measures range from 1 (for a perfect positive linear relationship) through 0 (for no linear relationship) to -1 (for a perfectly negative linear relationship (one where the line has a negative slope).