The application was sought by opposition parties and civic organisations who believe a bid to remove the president via a motion of no confidence can only succeed if members of parliament are allowed to vote in secret.
For a vote of no confidence to succeed, between 50 and 70 ANC MPs would need to vote with the opposition parties.
The UDM sought the initial application in the ConCourt which has since been backed by the EFF, IFP and the Institute for Security Studies.