Police Scotland confirmed a man had been arrested but not charged. He has been released pending further enquiries.
A statement read: “Police in Edinburgh can confirm that a second man has been arrested in connection with the murder of 48-year-old Bradley Welsh.
“The incident happened around 8pm on Wednesday, April 17, in Chester Street.
“This second man has been released pending further enquiries.
“This investigation is ongoing and officers are continuing to appeal for information.
“Anyone who can assist officers is asked to contact Police Scotland on 101, quoting incident number 3782 of April 17, or anonymously via Crimestoppers on 0800 555 111.”
Mr Welsh was shot outside his home in the city’s Chester Street. He died at the scene.
A murder investigation was launched and police forensics teams searched the area outside of his property for evidence.
Another man was arrested in connection with the murder on Tuesday and he too was released pending further enquiries.
Police said Mr Welsh was targeted outside his home after returning from training at Holyrood Boxing Gym, which he owned.
Mr Welsh’s family were inside the property at the time, initially unaware of what had happened.
Mourners left tributes at the scene and outside of Mr Welsh’s gym.
Many took to social media to speak of their upset, including Trainspotting author Irvine Welsh - a close friend and fellow Hibs supporter - who paid tribute and said his “heart is broken”.
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