A process for dry fractionation of a soft palm oil mid fraction (SPMF) into a final hard palm oil mid fraction (fHPMF-A) is disclosed. The process comprises: providing the solf palm oil mid fraction (SPMF), using the soft palm oil mid fraction (SPMF) as an input (IN1) to a first dry fractionation (FDF) to obtain an intermediate olein fraction (SPMF-O) and an intermediate stearin fraction (SPMF-S), using the intermediate olein fraction (SPMF-O) as an input (IN2) to an ultrasound assisted second dry fractionation (SDF) to obtain the final hard palm oil mid fraction (fHPMF-A) and a palm oil olein fraction (POO), wherein the ultrasound assisted second dry fractionation (SPF) comprises subjecting at least a part of the input (IN2) to ultrasonic treatment (US2). Also disclosed is a final hard palm oil mid fraction (fHPMF-A), a second hard palm oil mid fraction (sHPMF-B), a hard palm oil mid fraction mixture, and uses of these.