While monitoring a sample of apparently slowly rotating superficially normal bright late B and early A stars in the northern hemisphere, we have discovered that HD 67044 and HD 42035, hitherto classified as normal late B-type stars, are actually respectively a new chemically peculiar star and a new spectroscopic binary containing a very slow rotator HD 42035 S with ultra-sharp lines (vesini=3.7 kms−1) and a fast rotator HD 42035 B with broad lines. The lines of Ti ii, Cr ii, Mn ii, Sr ii, Y ii, Zr ii and Ba ii are conspicuous features in the high resolution SOPHIE spectrum (R=75000) of HD 67044. The Hg ii line at 3983.93 Å is also present as a weak feature. The composite spectrum of HD 42035 is characterised by very sharp lines formed in HD 42035 S superimposed onto the shallow and broad lines of HD 42035 B. These very sharp lines are mostly due to light elements from C to Ni, the only heavy species definitely present are strontium and barium. Selected lines of 21 chemical elements from He up to Hg have been synthesized using model atmospheres computed with ATLAS9 and the spectrum synthesis code SYNSPEC48 including hyperfine structure of various isotopes when relevant. These synthetic spectra have been adjusted to high resolution high signal-to-noise spectra of HD 67044 and HD 42035 S in order to derive abundances of these key elements. HD 67044 is found to have distinct enhancements of Ti, Cr, Mn, Sr, Y, Zr, Ba and Hg and underabundances in He, C, O, Ca and Sc which shows that this star is not a superficially normal late B-type star, but actually is a new CP star most likely of the HgMn type. HD 42035 S has provisional underabundances of the light elements from C to Ti and overabundances of heavier elements (except for Fe and Sr which are also underabundant) up to barium. These values are lower limits to the actual abundances as we cannot currently place properly the continuum of HD 42035 S. More accurate fundamental parameters and abundances for HD 42035 S and HD 42035 B will be derived if we manage to disentangle their spectra. They will help clarify the status of the two components in this interesting new spectroscopic binary.