A method of intracellular delivery of a substance of interest, including the step of using a maurocalcine-derived peptide vector for transporting said substance of interest into cells is described. The vector including a maurocalcine-derived peptide of sequence (I): Z-X1-X2-X3-X4-X5-X6-X7-X8-X9-X10-X11-X12-X13-X14-X15-X16-X17-X18-X19-X20-X21-X22-X23-X24-X25-X26-Z′, wherein X1 and X26 each represent a cysteine, X2 to X25 each represent an amino acid or are absent, X7, X10, X11, X12, X13, X14, X15 and X16 are always present, and X10, X11, X13 and X14, each represent a lysine or an arginine, and Z and/or Z′ are absent or each represent a sequence of 1 to 35 amino acids, with the exception of the peptide having the sequence SEQ ID NO:1 in the sequence listing attached in the annex.