A guidewire kit including a guidewire with a shaft having a curved steering section and including a straightener bounding a lumen for straightening at least the curved deflection section of the guidewire extending into the lumen for insertion of the tip and the curved deflection section of the guidewire into a needle inserted into a vessel of a patient. The straightener is of a length of at least 8 cm for obtaining an improved and more reliable steering effect of the curved steering section.