Rules for Decomposition to 2 NF
To simplify, say we have 

R(A,B,C,D)

AB -&gt; C
A  -&gt; D


Relation R is NOT in 2NF -- the KEY is {AB}, but {D} is dependent only on part of the key.

Now decomposition


Step 1.   R1 {ABC}  R2 {AD}
Done.


So, both R1 and R2 are in 6NF and therefore in 5,4,3,2,1. There is no in-between -- it may happen that in some specific example you may see "progress" 1, 2, 3, BCNF; but that is an exception, not the rule.


  ... looking at a systematic approach to move from 1 NF to 2 NF to 3
  NF to BCNF ...


is a common misunderstanding.