It means you have a problem. I don't have experience with this particular instrument, but I will suggest you begin by cleaning it (or the cuvette) very thoroughly. Then, make sure the instrument is working properly by measuring a standard.
You should validate the instrument and your setup by using a known quantity of DNA at a few concentrations as positive controls along with your blank (no added DNA).
Cleaning and blanking with the solvent should help but you haven't mentioned the values. Most instruments have some variations in readings even with the same sample. If you are seeing a value that is negative in fourth decimal place, for all practical purpose, you can consider it as zero.
You have to make sure that your cuvette is clear enough (there is no spot or something else on it),
afterward, check your blank (ddH2O) its absorbance must be 0.000 to get better result. if cuvette and blank OK, but you still get negative result, there is a problem with your samples, (may be any contaminants).
I am using this type Eppendorf bio-photo meter, as routine basis for my work but i never watch such "Negative" indicator. In that instrument there is lots of option for protein, ssDNA, dsDNA, RNA, Oligo etc. So, have to chose the perfect programs to measure specific things like dsDNA, RNA, protein etc.
When you do "Blank" with Dnase/Rnase free water, make sure about the dilution factor (portion of sample+ diluent). I always follow (7 ul DNA + 63 ul diluent) then push button for blank first and when its shows ok then you give sample. Never cross the cuvette maximum volume line. 70 ul volume is perfect, what i do.
Another, important thing is Validation & Calibration, supplier normally validate the instrument with standard known solution. So, hope you can find the way to make your work done and wish for a good result. :-)