diff --git a/docs/tools/agat_sp_fix_cds_phases.md b/docs/tools/agat_sp_fix_cds_phases.md
index e0a5236a..89c81a63 100644
--- a/docs/tools/agat_sp_fix_cds_phases.md
+++ b/docs/tools/agat_sp_fix_cds_phases.md
@@ -1,14 +1,50 @@
-# agat\_sp\_fix\_cds\_frame.pl
+# agat\_sp\_fix\_cds\_phases.pl
 
 ## DESCRIPTION
 
-This script aims to fix the cds phases.
+This script aims to fix the CDS phases.
+The script is compatible with incomplete gene models (Missing start, CDS
+multiple of 3 or not, i.e. with offset of 1 or 2) and + and - strand.
+
+How this script works?  
+AGAT uses the fasta sequence to verify the CDS frame.
+In case the CDS start by a start codon the phase of the first CDS piece is set to 0.
+In the case there is no start codon and: 
+  - If there is only one stop codon in the sequence and it is located at the last position, the phase of the first CDS piece is set to 0.
+  - If there is no stop codon, the phase of the first CDS piece is set to 0 (because sequence can be translated without premature stop codon).
+  - If there is/are stop codon(s) in the middle of the sequence we re-execute the check with an offset of +2 nucleotides:
+    - If there is only one stop codon in the sequence and it is located at the last position, the phase of the first CDS piece is set to 0.
+    - If there is no stop codon, the phase of the first CDS piece is set to 0 (because sequence can be translated without premature stop codon).
+    - If there is/are stop codon(s) in the middle of the sequence we re-execute the check with an offset of +1 nucleotide:
+        - If there is only one stop codon in the sequence and it is located at the last position, the phase of the first CDS piece is set to 0.
+        - If there is no stop codon, the phase of the first CDS piece is set to 0 (because sequence can be translated without premature stop codon).
+        - If there is/are still stop codon(s) we keep original phase and throw a warning. In this last case it means we never succeded to make a translation without premature stop codon in all the 3 possible phases.
+Then in case of CDS made of multiple CDS pieces (i.e. discontinuous feature), the rest of the CDS pieces will be checked accordingly to the first CDS piece.
+
+What is a phase?  
+For features of type "CDS", the phase indicates where the next codon begins
+relative to the 5' end (where the 5' end of the CDS is relative to the strand
+of the CDS feature) of the current CDS feature. For clarification the 5' end
+for CDS features on the plus strand is the feature's start and and the 5' end
+for CDS features on the minus strand is the feature's end. The phase is one of
+the integers 0, 1, or 2, indicating the number of bases forward from the start
+of the current CDS feature the next codon begins. A phase of "0" indicates that
+a codon begins on the first nucleotide of the CDS feature (i.e. 0 bases forward),
+a phase of "1" indicates that the codon begins at the second nucleotide of this
+CDS feature and a phase of "2" indicates that the codon begins at the third
+nucleotide of this region. Note that ‘Phase’ in the context of a GFF3 CDS
+feature should not be confused with the similar concept of frame that is also a
+common concept in bioinformatics. Frame is generally calculated as a value for
+a given base relative to the start of the complete open reading frame (ORF) or
+the codon (e.g. modulo 3) while CDS phase describes the start of the next codon
+relative to a given CDS feature.  
+The phase is REQUIRED for all CDS features.
 
 ## SYNOPSIS
 
 ```
-agat_sp_fix_cds_frame.pl --gff infile.gff -f fasta [ -o outfile ]
-agat_sp_fix_cds_frame.pl --help
+agat_sp_fix_cds_phases.pl --gff infile.gff -f fasta [ -o outfile ]
+agat_sp_fix_cds_phases.pl --help
 ```
 
 ## OPTIONS
@@ -27,7 +63,7 @@ agat_sp_fix_cds_frame.pl --help
 
 - **-o** or **--output**
 
-    Output GFF file.  If no output file is specified, the output will be
+    Output GFF file. If no output file is specified, the output will be
     written to STDOUT.
 
 - **-c** or **--config**