The blade tip is a particularly critical component of the high pressure turbine due to the hot overtip leakage gas being responsible for efficiency losses and thermal degradation, often limiting engine life. Squealer tip designs reduce the over-tip leakage mass flow, increasing efficiency, but the thin pressure side rims can be vulnerable to damage because of their large surface area and the difficulties of shielding them from hot overtip leakage flow. This paper considers a new approach to cooling these pressure side rims, by employing an inclined slot inside a recessed step. Compared to conventional cooling strategies, in which coolant is provided by multiple cylindrical holes, the slot feature improves cooling effectiveness by more than 50% in key regions of the pressure side rim, whilst also allowing for a substantial reduction in coolant mass flow. The concept design is developed and explored using Computational Fluid Dynamics (CFD) calculations, and the performance is validated experimentally in a linear cascade with representative Mach and Reynolds numbers.