A 22-year-old man from Birmingham has been arrested on suspicion of collection of information likely to be used by a terrorist.
The man was detained by West Midlands Counter Terrorism Unit officers at his home address on Thursday.
His arrest is not related to the arrest of a 21-year-old man in the Alum Rock area of the city on Tuesday, police said.
The 22-year-old was released on bail after questioning.
Neither arrest was made in response to any immediate threat, they added.
Det Insp Alan McSharry said both offences were of a serious nature.
"Officers from the West Midlands Counter Terrorism Unit and local neighbourhood officers will continue to work with our communities to combat terrorism," he added.