Over the last decade, there was very strong growth in the demand for vegetable oils and fats (+ 4.6% per year) and the oils extracted from oil palm fruits greatly contributed to satisfying those needs. Food demand continues to increase, as do traditional uses (cosmetics and oleo chemistry). A new demand for use as bio fuel also needs to be taken into account (1% of current consumption). For oil palm, high-yielding planting material that is as resistant as possible to diseases will be part of the answer proposed by breeders. The breeding scheme primarily involves a reciprocal recurrent selection scheme (RRS) which has been adapted to the biological constraints of the oil palm. The RRS recommended by CIRAD uses, in the form of hybrids, the heterosis effect obtained by crossing origins with complementary characteristics (group A) x (group B). It is also possible to include pedigree selection phases (A self or B self), which cannot really be considered as part of RRS, but the two strategies are complementary. In the oil palm, the general combining ability (GCA) for yield of a parent can only be known by assessing the value of the families it generates. However, some parental traits are heritable enough for it to be efficient to select them: vertical growth, mesocarp/fruit percentage, oil/mesocarp and the number of bunches produced. In order to assess the parental combining ability, we propose a scheme that makes it possible to test all family and each parent. Such a design makes it possible to evaluate the value of all the crosses by removing the inherent trial effect, and the planting year effect. It makes it possible to compare all the parents used in the design with each other. The share of variability explained by an additive model has been calculated. As an example, the Aek Loba design is described. Our study focuses on the mature period for the first 17 trials that have been observed up to 8 years (254 crosses, 114 parents in group A, and 112 in group B). At the p