This paper is concerned with the static output feedback stabilisation of Markov jump systems. Transition probabilities are assumed to be incomplete, namely, they may be known, uncertain with known lower and upper bounds and unknown. To linearise the nonlinearities induced by unknown transition probabilities, a linearisation is developed. To solve the static output feedback problem by means of linear matrix inequalities, a constructive method is proposed to separate the controller gain matrices from Lyapunov variables. Based on the linearisation and the separation, sufficient conditions are established to guarantee that the closed-loop system is stochastically stable by the designed static output feedback controller. The obtained results are further extended to deal with norm-bounded or polytopic uncertainties on system matrices. Numerical examples are given to demonstrate the effectiveness of the proposed method.