The remaining conjoined twin, Jodie, in a Manchester hospital was yesterday making a "rapid recovery" and had started breathing without the help of a ventilator, according to her medical team.
A spokeswoman for St Mary's Hospital, Manchester, where the operation to separate her from her weaker twin, Mary, took place this week, said: "Jodie is well and is making a rapid recovery.
"Since last night she has been breathing without support and has started feeding normally."
The spokeswoman added that it was still a critical time for the baby girl and she would continue to be monitored closely.
Her parents are believed to be keeping a constant vigil at her bedside in the intensive care unit of the hospital.
The marathon 20-hour operation to separate the twins, who were born with fused spines which left them joined at the abdomen, was completed at 5 a.m. on Tuesday and led to the expected death of Mary, who relied on her sister's organs for survival.
It was opposed by the parents of the twins who are strict Catholics from the island of Gozo near Malta and believed the fate of their daughters should be left in the hands of God.
Surgeons took their case to court and won the right to operate.
Experts on conjoined twins said the operation would take a huge toll on Jodie and her life would be in the balance for at least 72 hours afterwards.
If she survives the post-operative period, Jodie will face years of corrective surgery and skin grafts to help her achieve a near-normal life.
Jodie and Mary are pseudonyms for the twins.