Hydrolyzes diadenosine 5',5'''-P1,P4-tetraphosphate to yield ADP. H2O + P(1),P(4)-bis(5'-adenosyl) tetraphosphate = 2 ADP + 2 H(+) Co(2+) is a strong stimulator (100-fold increase in rate of hydrolysis). Mn(2+), Cd(2+), Ni(2+), Mg(2+) and Ca(2+) are weak stimulators; the two latter act synergistically with Co(2+). Monomer. Belongs to the Ap4A hydrolase family.