"each unique" is correct and usable in written English.
You can use it to refer to the individual qualities of two or more things. For example, "The musicians each had a unique style of playing."
Inside each unique dress is printed a poem by Alvarez.
for each unique spikes (how many depends on corrRudolph).
Each unique design has its own advantages and limitations.
Each unique defect structure is defined as an object.
NBC will subsequently announce how long each unique user stayed on the site.
Each unique EMG T-shirt will incorporate offcuts from up to six fashion houses.
Dozens of rambling century-old houses line the narrow streets -- each unique and ornate.
It consists of thousands of porcelain crabs, beautifully realistic, eerily similar and yet each unique.
Specific primers targeting each unique sequence of interest were designed by hand.
For the applied symmetries, views are presented for each unique asymmetric subunit (boxed).
Each unique variant (indel and structural variants) was visually confirmed using IGV30.
