# Row normalization before correlation analysis for abundance data

I work with datasets in which protein abundances are reported across samples. I have some measurements of biological samples that should be more or less equal in protein abundance.

After getting the data as intensities, they are normalized by subtracting the log$_2$ median of each sample. If I plot these normalized and log transformed intensities, I get a Pearson correlation of around 0.98. But when I divide each row by the row median and log$_2$ transform of the ratio, I get a Pearson correlation of about 0.3. I need to process my data by row normalizing them.

So I am clearly doing something very wrong when performing the correlation analysis after row normalization. How do I perform a correlation analysis on these values?