The move is a further sign that CBI is delivering on its promise of allowing the inflation rate to influence the forex rate.
CBI announced the rate at 42,110 rials on Saturday from 42,090 on Thursday. The rate was first raised from the unified rate of 42,000 rials to 42,050 on Monday, the central bank's website reported.
A similar attempt to unify the exchange rate in 2012 fell flat when the rate was fixed at 12,260 rials without due attention to market mechanisms. Although analysts also object to the current rate as unrealistic, its flexibility is expected to appease pro-market forces, Financial Tribune reported.
The forex unification came on the heels of a sharp slide in the value of rial.
According to CBI measures, the US dollar for all purposes, including imports, travel, overseas students and research projects, is being offered by the government at the unified rate.
At present, the exchange rate for the greenback has increased by 110 rials since the rate unification, meaning that it has risen by 0.2% in 45 days.
According to Tehran Chamber of Commerce, Industries, Mines and Agriculture, euro has lost 26,000 rials or nearly 5% of its value against the rial during the same period.
On Saturday, the European currency's exchange rate lost 149 rials, with each euro being quoted for 49,109 rials. The British pound's exchange rate lost 205 rial, with each pound being exchanged for 56,330 rials.
Black market rates tend to be quoted much higher. Latest media reports from Thursday indicated that the US dollar was exchanged in the neighborhood of 63,000 rials.
Ahmad Anaraki Mohammadi, a member of Majlis Economic Commission, on Saturday also supported the exchange rate's movement in line with inflation. In an interview with IBENA, however, he said that changing the official rate more than once a year is not prudent since it would signal market instability.
CBI Governor Valiollah Seif last week hinted at an exchange rate hike, saying that it would have 5-6% flexibility until the end of the current fiscal year on March 20, 2019.
The government's forex decisions have recently come under private sector fire, with the business community panning the unified rate as too unreal and forex controls as too suffocating.
It has also complained the lack of an open forex market trading that has been driven underground.
Masoud Khansari, the head of TCCIM, among others, has called for a series of changes to the forex policy, including the establishment of a "secondary market".