We present a new harmonic development of the long-periodic band of the Earth tide-generating potential (TGP). It updates the corresponding part of the previous TGP expansion, KSM03, and includes 38 terms of period longer than about 18 years (yr) and amplitude not less than 10^-8 m²·s^-2. The development is made through a modified spectral analysis of the TGP numerical values tabulated over more than 30000 yr (13201 BC-17191 AD). The latest JPL NASA's long-term numerical ephemeris DE441 is used to source the Moon, the Sun, and major planets' coordinates. For comparison, the KSM03 series was done on the basis of an older DE406 ephemeris and over a shorter time interval of 2000 yr (1000-3000). As a result of using an extended time span, several new long-periodic waves in the Earth TGP were found and most of the other terms are updated. In particular, a relatively large term of amplitude of 3 × 10^-5 m²·s^-2 and a period of approximately 7.4 kyr is revealed. Several new waves of period close to 18.61 yr (the period of the lunar nodal cycle, LNC) are separated from the main LNC term. The effect of the general precession in longitude (of a 25.7 kyr period) on the Earth TGP for the first time is evaluated. As a result, a number of updated TGP terms include the precession rate in their arguments. A new catalogue of the long-periodic terms in the Earth TGP spectrum in both standard HW95 and KSM03 format is released.