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He died at 2 pm in a hospital in the capital, said his nephew Advocate Mahfuz.
He was admitted to the hospital three days back and found Covid-19 positive on Thursday.
The former MP was undergoing treatment at the Intensive Care Unit (ICU) of the hospital.
Abu Hena was elected to parliament from Rajshahi-3 as a Bangladesh Nationalist Party candidate in 1996 and 2001.
Meanwhile, Bangladesh recorded 1,531 new coronavirus cases and 14 deaths in 24 hours until Saturday morning amid apprehensions about a second deadly wave of Covid-19 this winter.
Fatalities from the virus outbreak in the country reached 6,173 with a death rate of 1.43 percent.
The caseload rose to 430,496 as of Saturday, the Directorate General of Health Services said.
Also read: Covid-19: Bangladesh sees 1531 new cases, 14 deaths in 24 hrs