Remote state preparation is a secure and faithful method for transmitting known quantum states by means of local operation and classical communication. Existing protocols in the general case succeed just with probabilities of less than 100%. In this paper, we design a protocol to remotely prepare the most general single-qubit state that always succeeds. To achieve unit success probability, the preparer is allowed to use additional local resources and implement adaptive measurements. Our protocol is meaningful because the most expensive resource, i.e. the quantum channel previously shared between the preparer and the receiver, remains the same as in the original protocol (Pati 2000 Phys. Rev. A 63 014302), which, however, succeeds only half the time.