Thread: port increments despite having been previously closed??

In one windows application I am developing I am periodically:
opening a socket with socket()
then I call connect (to server IP and port)
then i exchange some data with send/recv
then I close the socket with

Code:

shutdown(i, SD_BOTH)
closesocket(i)

appearantly all calls are performed correctly
but what happens is that at every successive connect I am assigned a different (increasing by one) port

Is that normal or do I have to suspect that the previous port was not set free correctly by shutdown+close?