The invention concerns the use of a compound of formula (I), wherein: A1 is the radical corresponding to D- or L-Ser; A2 is the radical corresponding to D- or L-Asp or Glu; A3 is the radical corresponding to D- or L- Lys, Arg or Orn; A4 is the radical corresponding to D- or L- Pro; R1 and R2 selected independently among H, C1-C12 alkyl substituted or not;, C7-C20 arylalkyl substituted or not, R4CO, R4COO, R4 being C1-C12 alkyl substituted or not, C7-C20 arylalkyl substituted or not, including among the substitutions OH, NH2 or COOH; X1 and X2 are peptide or pseudopeptide bonds; X3 is CO or CH2 and R3 is OH, NH2, C1-C12 alkoxy or NH-X4-CH2-Z; X4 is a linear or branched C1-C12 hydrocarbon; Z is H, OH, CO2H or CONH2, or the corresponding tripeptides comprising the radicals A1, A 2, A3; and their pharmaceutically acceptable salts, for producing a medicine designed to treat pathologies likely to benefit from stimulation of angiogenesis.