A largely extended X-ray emission was discovered around the pulsar PSR J1357 - 6429 with the Suzaku deep observations .
The pulsar , whose characteristic age is 7.3 kyr , is located within the TeV \gamma -ray source HESS J1356 - 645 .
The extended emission is found to have a 1 \sigma X-ray size of \sim 4 arcmin , or \sim 3 pc at 2.4 kpc , with a small offset from the pulsar .
Its X-ray spectrum is well reproduced by a simple power-law model with a photon index of 1.70 _ { -0.06 } ^ { +0.07 } .
No significant spatial variation was found for the X-ray photon index as a function of distance from the pulsar .
We conclude that the extended emission is associated to the pulsar wind nebula of PSR J1357 - 6429 .
This is a new sample of largely extended nebulae around middle-aged pulsars .
We discuss the evolution of this PWN according to the relic PWN scenario .