Using X-ray data from the Rossi X-Ray Timing Explorer ( RXTE ) , we report the pulse timing results of the accretion powered high mass X-ray binary ( HMXRB ) pulsar 4U 1907+09 covering a time span of almost two years . We measured three new pulse periods in addition to the previously measured four pulse periods . We are able to connect pulse arrival times in phase for more than a year . The source has been spinning down almost at a constant rate with a spin down rate of \dot { \nu } = ( -3.54 \pm 0.02 ) \times 10 ^ { -14 } Hz s ^ { -1 } for more than 15 years . Residuals of pulse arrival times yield a very low level of random walk noise strengths \sim 2 \times 10 ^ { -20 } rad ^ { 2 } sec ^ { -3 } on a time scale of 383 days , which is four decades lower than that of the HMXRB pulsar Vela X-1 . The noise strength is only a factor of 5 greater than that of the low mass X-ray binary pulsar ( LMXRB ) 4U 1626-67 . The low level of the timing noise and the very stable spin down rate of 4U 1907+09 makes this source unique among the HMXRBs , providing another example , in addition to 4U 1626-67 , of long term quiet spin down from an accreting source . These examples show that the extended quiet spin down episodes observed in the anomalous X-ray pulsars ( AXPs ) pulsars 1RXS J170849.0-400910 and 1E 2259+586 do not necessarly imply that these sources are not accreting pulsars .