The J’ dependencies of energy and line width of the (NaK)-Na-23-K-39 B-1 Pi(upsilon’ = 30-43, J’) <-- X(1) Sigma(+)(upsilon" = 2, J’) transitions are measured up to the breaking-off points, where NaK dissociates to the Na(3s(2)S(1/2)) + K(4p(2)P(3/2)) atoms. Line broadenings are observed for transitions to the B-1 Pi(upsilon’ = 30, J’ greater than or equal to 42), (upsilon’ = 31, J’greater than or equal to 35), (upsilon’ = 32, J’ greater than or equal to 27), (upsilon’ = 33, J’ greater than or equal to 14), and (upsilon’ greater than or equal to 34, all J’) levels, and are attributed to the predissociation via the c(3) Sigma(+) state to the Na(3s(2)S(1/2)) + K(4p(2)P(1/2)) atoms. The (upsilon’, J’) dependence of the predissociation threshold is attributed to the potential barrier due to rotation. Below and near the threshold, a series of the perturbation centers which converge to the predissociation threshold is observed for each upsilon’, and the perturbing state is identified as the c(3) Sigma(+) state. Rotational perturbations are observed also above the predissociation threshold, and the perturbing state is identified as the b3 Pi(1) state. The line widths are observed to change drastically around the maximum perturbation, and this is identified as originating from the interference effect which arises because both the B-1 Pi and b(3) Pi(1) states interact with the dissociative continuum of the c(3) Sigma(+) state. In the transitions to levels near the breaking-off points of the B-1 Pi(upsilon’ greater than or equal to 37), the line splittings into two lines are observed for each J’. This splitting is identified as originating from the S-uncoupling interaction between the B-1 Pi and b(3) Pi states at a long internuclear distance. Similar line splittings an observed for the B-1 Pi(upsilon’ = 30, all J’) levels, but are not observed for upsilon’ = 31-36. An accidental coincidence of the level energies of the B-1 Pi(upsilon’ = 30) and b(3) Pi(upsilon) levels is presumed, and the origin of the line splitting is identified as the S-uncoupling interaction. This is confirmed by the analysis of the hyperfine structures observed for the split lines.