Context : Abundances of iron-peak and \alpha -elements are poorly known in Orion , and the available measurements yield contradictory results .

Aims : We measure accurate and homogeneous elemental abundances of the Orion subgroups ONC and OB1b , and search for abundance differences across the Orion complex .

Methods : We present flames/uves spectroscopic observations of 20 members of the ONC and OB1b .
We measured radial velocity , veiling , effective temperature using two spectroscopic methods , and determined the chemical abundances of Fe , Na , Al , Si , Ca , Ti , and Ni using the code MOOG .
We also performed a new consistent analysis of spectra previously analyzed by our group .

Results : We find three new binaries in the ONC , two in OB1b , and three non-members in OB1b ( two of them most likely being OB1a/25 Ori members ) .
Veiling only affects one target in the ONC , and the effective temperatures derived using two spectroscopic techniques agree within the errors .
The ONC and OB1b are characterized by a small scatter in iron abundance , with mean [ Fe/H ] values of -0.11 \pm 0.08 and -0.05 \pm 0.05 , respectively .
We find a small scatter in all the other elemental abundances .
We confirm that P1455 is a metal-rich star in the ONC .

Conclusions : We conclude that the Orion metallicity is not above the solar value .
The OB1b group might be slightly more metal-rich than the ONC ; on the other hand , the two subgroups have similar almost solar abundances of iron-peak and \alpha -elements with a high degree of homogeneity .