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I have the problem, that the energy change between the current step and the last step as printed in the OSZICAR file is quite large. The energy change is merely one order of magnitude smaller than the total energy:

N E dE d eps ncg rms rms(c)
DAV: 1 -0.337384527443E+01 -0.33738E+01 -0.38860E+02 45 0.874E+01
DAV: 2 -0.372193260701E+01 -0.34809E+00 -0.34053E+00 55 0.834E+00
DAV: 3 -0.372718459046E+01 -0.52520E-02 -0.52361E-02 45 0.104E+00
DAV: 4 -0.372718606241E+01 -0.14719E-05 -0.14719E-05 65 0.167E-02
DAV: 5 -0.372718606243E+01 -0.20602E-10 -0.43459E-10 45 0.984E-05 0.183E-01
DAV: 6 -0.372585375602E+01 0.13323E-02 -0.72293E-05 45 0.424E-02 0.121E-01
DAV: 7 -0.372495270376E+01 0.90105E-03 -0.21528E-04 40 0.756E-02 0.586E-03
DAV: 8 -0.372491974393E+01 0.32960E-04 -0.15649E-06 50 0.649E-03 0.219E-03
DAV: 9 -0.372491428960E+01 0.54543E-05 -0.52719E-07 25 0.360E-03 0.106E-04
DAV: 10 -0.372491432781E+01 -0.38211E-07 -0.19947E-08 20 0.648E-04
1 F= -.37249143E+01 E0= -.37250084E+01 d E =-.372491E+01
N E dE d eps ncg rms rms(c)
DAV: 1 -0.372742550250E+01 -0.25112E-02 -0.11675E-03 40 0.175E-01 0.545E-03
DAV: 2 -0.372742450867E+01 0.99382E-06 -0.22741E-06 40 0.121E-02
2 F= -.37274245E+01 E0= -.37275557E+01 d E =-.251018E-02
N E dE d eps ncg rms rms(c)
DAV: 1 -0.373062917827E+01 -0.32037E-02 -0.68815E-03 40 0.430E-01 0.131E-02
DAV: 2 -0.373062152583E+01 0.76524E-05 -0.13910E-05 40 0.303E-02 0.839E-03
DAV: 3 -0.373061918015E+01 0.23457E-05 -0.43301E-06 40 0.111E-02 0.692E-04
DAV: 4 -0.373061897251E+01 0.20765E-06 -0.89287E-09 20 0.635E-04
3 F= -.37306190E+01 E0= -.37308392E+01 d E =-.570464E-02
N E dE d eps ncg rms rms(c)
DAV: 1 -0.373078412969E+01 -0.16495E-03 -0.57545E-04 40 0.125E-01 0.382E-03
DAV: 2 -0.373078359898E+01 0.53071E-06 -0.12548E-06 40 0.918E-03
4 F= -.37307836E+01 E0= -.37310292E+01 d E =-.586927E-02

Does anybody know how I can achieve that the calculation stops only after dE is much much smaller?

have you set NSW, have you modified the convergence parameters (EDIFF, EDIFFG)?