When Dr Norman objected to interventions by Mr Finlayson on the extent of his questions, Mr Finlayson said: "You're a member of the committee, not Judge Judy.''
Dr Norman got very few answers from Mr Fletcher about the police investigation into the unlawful spying on internet mogul Kim Dotcom.
Mr Fletcher said the matter was before the Independent Police Conduct Authority, but he said the decision by GCSB staff not to co-operate with the police inquiry had been a "matter for the individuals.''
He refused to answer Dr Norman's questions about whether the GCSB used Prism and other spyware exposed by the NSA defector Edward Snowden.
Mr Fletcher and SIS director Warren Tucker appeared together, but Dr Tucker's presentation and questions came first.
He disclosed that the SIS's help had been sought by the Defence Force after a high number of casualties in Afghanistan last year.