There can be significant uncertainty as to the safety of novel or complex aviation systems, such as Remotely Piloted Aircraft Systems (RPAS). Current aviation safety assessment and compliance processes do not adequately account for uncertainty. The aim of this research is to support more objective, transparent, systematic and consistent regulatory outcomes in relation to the safety assessment of such systems. The objective of this work is to provide a systematic means of accounting for the various uncertainties inherent to any System Safety Assessment (SSA) process. The paper first defines the system safety compliance process and its modification to account for uncertainty. The SSA process, its various outputs, and associated uncertainties are defined and then applied to a generic RPAS. A Bayesian Belief Network (BBN) is adopted that facilitates a more comprehensive treatment of the uncertainty in each of the outputs of a typical SSA process. A case study of a generic RPAS is used to illustrate the features of the new approach. The adoption of the Proposed SSA approach would allow for the high uncertainty associated with the safety assessment of novel or complex aviation systems, such as RPAS, to be taken into consideration. Such an approach would enable the risk-based regulation of the sector.