During process of protein synthesis we need AUG Codon to start translation .As we know this codon codes for Methionine amino acid so can we say that every protein starts with Methionine amino acid ?
No, not every protein starts with a methionine. When the methionine is removed, it is called N-terminal methionine excision. Abstract excerpt below:
N-terminal methionine excision (NME) is the major proteolytic pathway responsible for the diversity of N-terminal amino acids in proteins. Dedicated NME components have been identified in all organisms, in all compartments in which protein synthesis occurs: cytoplasm, plastids and mitochondria. Recent studies have revealed that NME is regulated at various levels and plays an important role in controlling protein turnover. NME is essential in Eubacteria and lower eukaryotes and is the target of many natural and synthetic inhibitors. Such inhibitors have considerable potential for use in the treatment of various human diseases, from cancer to bacterial and parasitic infections.
And from a recent review focusing on the methionine aminopeptidase enzyme that cleaves the first methionine:
Protein synthesis is initiated by methionine in eukaryotes and by formylmethionine in prokaryotes. N‐terminal methionine can be co‐translationally cleaved by the enzyme methionine aminopeptidase (MAP). When recombinant proteins are expressed in bacterial and mammalian expression systems, there is a simple universal rule that predicts whether the initiating methionine will be processed by MAP based on the size of the residue adjacent (penultimate) to the N‐methionine.
Mitochondria and other organelles also have different start codons. Their alternate start codons are well-characterized (AUA and AUU in humans and mainly - but not exclusively - GUG and UUG in prokaryotes).