Extending the RNN Transducer (RNNT) to recognize multi-talker speech is essential for wider automatic speech recognition (ASR) applications. Multi-talker RNNT (MT-RNNT) aims to achieve recognition without relying on costly front-end source separation. MT-RNNT is conventionally implemented using architectures with multiple encoders or decoders, or by serializing all speakers' transcriptions into a single output stream. The first approach is computationally expensive, particularly due to the need for multiple encoder processing. In contrast, the second approach involves a complex label generation process, requiring accurate timestamps of all words spoken by all speakers in the mixture, obtained from an external ASR system. In this paper, we propose a novel alignment-free training scheme for the MT-RNNT (MT-RNNT-AFT) that adopts the standard RNNT architecture. The target labels are created by appending a prompt token corresponding to each speaker at the beginning of the transcription, reflecting the order of each speaker's appearance in the mixtures. Thus, MT-RNNT-AFT can be trained without relying on accurate alignments, and it can recognize all speakers' speech with just one round of encoder processing. Experiments show that MT-RNNT-AFT achieves performance comparable to that of the state-of-the-art alternatives, while greatly simplifying the training process.