\textit{N. L. Johnson} and \textit{S. Kotz}, Commun. Stat., Theory Methods A6, 485-496 (1977; Zbl 0382.62040) introduced the (k-1)-iteration Farlie- Gumbel-Morgenstern (FGM) distribution \[ H_{1k}=FG+\sum^{k}_{j=1}\alpha_{1j}(FG)^{[j/2]+1}(\bar F\bar G)^{[(j+1)/2]} \] where F and G are the marginal distributions. \textit{J. S. Huang} and \textit{S. Kotz}, Biometrika 71, 633-636 (1984; Zbl 0555.62050), found the natural parameter space of \(H_{12}\) for arbitrary absolutely continuous distributions F and G. The present paper extends the latter result to arbitrary continuous distributions F and G and proposes another (k-1)-iteration FGM distribution: \[ H_{2k}=FG+\sum^{k}_{j=1}\alpha_{2j}(FG)^{[(j+1)/2]}(\bar F\bar G)^{[(j/2)+1]}. \] Further, the conditions are found on F and G under which \(H_{1k}\) and \(H_{2k}\) have the same natural parameter space. The multivariabe case and some other properties are also discussed.