The company, whose stock posted a 60 per cent jump last month after starting trials at the Southern General Hospital, wants to use stem cells to treat stroke patients.
An independent data safety monitoring board met to review the status of the first patient in the trial 28 days after the treatment.
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Hide AdThe board decided that ReNeuron can now continue with its trial using a further three patients.
Chief executive Michael Hunt said: "We are delighted that the stroke clinical trial will now move forward to the next milestone. It is both encouraging and reassuring to hear that no safety issues have been observed."