The phase relations on the B-rich side of stoichiometric TiB2 were experimentally studied. It was found that a peritectic four-phase reaction liquid + AlB12 double left right arrow AlB2 + TiB2 occurs at a temperature between 1073 and 1173 K. Part of the Al-rich corner of the Al -Ti-B phase diagram was calculated and isothermal sections at 973, 1073, 1173 and 1273 K are presented. The peritectic four-phase reaction was calculated to occur at 1150 K in agreement with the experimental results. The Al-rich part of the binary Al -B system was reassessed. A eutectic reaction liquid double left right arrow AlB2 + (Al) was confirmed to occur at 932.9 K and 0.055 at.% B and a peritectic reaction liquid +AlB12 double left right arrow AlB2 concluded to happen at 1150 K (slightly above the four-phase reaction) and 0.60 at.% B, which is at a lower temperature than previously reported.