Single-step genomic predictions need the inverse of the part of the additive relationship matrix between genotyped animals (A(22)). Gains in computing time are feasible with an algorithm that sets up the sparsity pattern of A(22)(-1) (SP algorithm) using pedigree searches, when A(22)(-1) is close to sparse. The objective of this study is to present a modification of the SP algorithm (RSP algorithm) and to assess its use in approximating A(22)(-1) when the actual A(22)(-1) is dense. The RSP algorithm sets up a restricted sparsity pattern of A(22)(-1) by limiting the pedigree search to a maximum number of searched branches. We have tested its use on four different simulated genotyped populations, from 10000 to 75000 genotyped animals. Accuracy of approximation is tested by replacing the actual A(22)(-1) by its approximation in an equivalent mixed model including only genotyped animals. Results show that limiting the pedigree search to four branches is enough to provide accurate approximations of A(22)(-1), which contain approximately 80% of zeros. Computing approximations is not expensive in time but may require a great amount of memory (at maximum, approximately 81min and approximately 55Gb of RAM for 75000 genotyped animals using parallel processing on four threads).