BE36 PLT ON IFR DEP OBSERVED ANOTHER ACFT PASS 300 FT OVER THE TOP OF HIM BEFORE HE COULD TAKE EVASIVE ACTION. THE DEPT CTLR DID ASK HIM TO CLIMB FASTER JUST PRIOR TO THE TWO ACFT PASSING. HOWEVER; HE ADVISED THAT HE WAS ALREADY AT MAX CLIMB.

Narrative

ON NOV/MON/01; MY ACFT; A BE36/G; WAS CLRED FOR TKOF AROUND XA45 TO XA50 LCL TIME FROM BUR RWY 8. I WAS ON A TWR ENROUTE IFR FLT PLAN FROM BUR TO CNO. I WAS ASSIGNED THE ELMOD 5 DEP; AND THEN THE BURL6 TER ROUTING TO CNO INITIAL CLIMB TO 4000 FT WITH A FINAL ALT OF 5000 FT TO FOLLOW WITHIN 10 MINS. A FEW MOMENTS AFTER I CLRED THE DEP END OF THE RWY AND WAS ROLLIN ONTO THE SID DEFINED HEADING OF 120 DEGS; I WAS HANDED OFF TO SOCAL DEP. I CALLED AND WAS IMMEDIATELY CLRED TO 5000 FT. ABOUT TWO MINS LATER; AS I WAS CLBING THROUGH 3000 FT I WAS DIRECTED BY SOCAL TO 'INCREASE RATE OF CLB.' I RESPONDED THAT I WAS PRESENTLY DOING MY ACFT'S MAX RATE OF CLB: 800 TO 1000 FPM. I DID NOT GET A RESPONSE FROM SOCAL ON THAT. ABOUT 30 SECS AFTER THAT; I SAW THE OTHER ACFT; A SILVER-MIDDLE WEIGHT TWIN; WITH TURBINE ENG CONVERSIONS; AND A UNIQUE TAIL THAT HAS DUAL OVAL SHAPED VERTICAL STABILIZERS AT THE ENDS OF THE HORIZONTAL STABILIZER; PASS IN THE OPPOSITE DIRECTION; NO MORE THAN 200 TO 300 FT OVERHEAD. I WAS SOMEWHERE IN THE AREA OF DARTS INTERSECTION; HEADING SOUTHWEST AND JOINING V186. THE OTHER ACFT WAS ON A WESTERLY HEADING; IT APPEARED TO BE IN LEVEL FLT. I REALIZE THAT IN VMC; EVERYONE IS ON 'SEE AND AVOID;' AND I DID SEE AND AVOID THE OTHER ACFT; AS I AM HERE TO TELL ABOUT IT. BUT; I DIDN'T APPRECIATE BEING TOLD TO INCREASE MY RATE OF CLB DIRECTLY INTO THE OTHER ACFT'S PATH. IF MY ACFT HAD BEEN ABLE TO INCREASE ITS RATE OF CLB AS THE CTLR HAD REQUESTED; I WOULD HAVE BEEN MUCH CLOSER TO THE OTHER ACFT WHEN IT PASSED OVERHEAD; MAYBE EVEN COLLIDED WITH IT. I DON'T THINK THE CLTR EVEN KNEW THE OTHER ACFT WAS EVEN THERE. I GOT NO TFC CALL. IT WAS A TOTAL SURPRISE. ON MY PART; I SHOULD HAVE SEEN THE ONCOMING ACFT SOONER; I SUPPOSE I WAS TOO INTENT ON LOOKING AT THE NAVIGATION INSTRUCTIONS AS I WAS JOINING V186.