Face of Nation : The Ministry of Defence (MoD) said the behaviour was “not fitting of the high standards we expect”.
When the footage was posted on social media, Mr Corbyn said he was shocked and called for an investigation.
Labour has been asked for comment on the latest development.
The short clip showed four paratroopers in uniform firing before the camera panned to the target, a large portrait of the Labour leader.
An investigation was launched into the incident in April.
The four soldiers seen firing, as well as the soldier filming, received reprimands with two being demoted, according to The Sun.
An MoD spokeswoman said: “The Army has carried out a thorough investigation into this incident and has implemented disciplinary action against the individuals found guilty of misconduct.
“This behaviour was not fitting of the high standards we expect of our personnel, and we are always prepared to take action when our procedures are not adhered to correctly.”
It is not known when the footage was filmed.
It is believed the clip first circulated on Snapchat before being posted on Twitter.
