A new Δh method for finding the asymptotic normalization coefficient (ANC) was recently proposed by the author (2021). It was shown that the denominator of the re-normalized scattering amplitude f˜l includes the factor dl(E)=Δl(E)+hr(E)−h(η), where Δl(E) is the nuclear interaction part of the effective-range function (ERF) and Δh(E)=hr(E)−h(η) is the difference of the related Coulomb terms. Here hr(E)=Reh(η) for E>0, η=1/aBk is the Sommerfeld parameter, aB is the Bohr radius. The equation dl(E)=0 determines the f˜l poles at E=−ε (ε is a binding energy). In the present paper to calculate Δh(−ε) the function hr(E) is analytically continued to E<0. For this the series of hr(E) in powers of (aBk)2 which converges if (aBk)2<1 should be used. It is found that the first dominant term (aBk)2/12 of the asymptotic series has(E) is the same for hr(E) and h(η) (at E<0 for h(η)) when E→0. The subtraction of this dominant term from both hr(E) and h(η) simplifies the Δh(−ε) calculation. Here the Δh method applies to the ground and first excited S-wave bound states of 16O (16O↔4He+12C) which meet the condition |aBk|2<1. For 16O the standard ERF method does not work due to the large product Z1Z2 of the 4He and 12C charges. For the P− and D- wave 16O states the binding energies ε are so small that the approximate Δ method, when dl(E)≈Δl(E), is valid. ANCs for the ground and first excited P-wave bound states of 7Be (7Be↔3He+4He) are also calculated by polynomial fitting the sum Δl(E)+hr(E) up to E2 in an analogy with the ERF method. The results for Δh and EFR methods are close to each other. For this system aBκ>1 and the Δh method has no advantages over the standard ERF method. The Δh method opens up a new direction for systems with large Z1Z2 values when the ERF method no longer works.