Kunrei-siki (訓令式) is the official system of Japanese romanization, as enshrined in ISO 3602 (1989). The name is taken from the two Cabinet Orders (Jp. kunrei) that decreed it, the first in September 21, 1937, the second repeating the same decree on December 29, 1954. However, despite this official status and the fact that most Japanese are more comfortable in Kunrei, the de facto standard -- especially in any publications geared towards foreigners -- remains Hepburn. This is partly since General Douglas MacArthur, head of the post-WW2 occupation, considered Kunrei tainted by the militarism of the era, being entirely Japanese-crafted and also employed by the Imperial Japanese Army and Navy.

Kunrei is at heart a slightly modified version of the older Nippon-siki romanization. While broadly similar to Hepburn, it values regularity over English pronunciation and reduces all the 3-letter syllables of Hepburn back into line with the other 2-letter syllables. This makes the conversion easy for the Japanese, who can just mentally map the kana table to Roman letters, but makes the pronunciation of many words impossible for the uninitiated with renderings like Huzi for Fuji 富士 and zyûzyutu for jujutsu 柔術.

Another problem with Kunrei is that it is difficult to use for some newly created kana like ティ and フィ, as used in loanwords like パーティ "party" and フィルム "film". In Hepburn these would be logically represented as pâti and firumu, accurately reflecting the pronunciation, but Kunrei already has a "ti" reserved for the Hepburn sound chi and doesn't believe in the existence of "f"; for ティ the only solution is to use an apostrophe, pât'i, and for フィ it's the even more bizarre hwirumu. (Then again, a better solution might be to just use the original English form and stick with party and film.)

At any rate, here is a complete table for mapping hiragana to Kunrei:

あ a   か ka   さ sa   た ta   な na   は ha   ま ma  や ya  ら ra  わ wa ん n 
い i   き ki   し siti   に ni   ひ hi   み mi         り ri  ゐ(i)
う u   く ku   す su   つ tu   ぬ nu   ふ hu   む mu  ゆ yu  る ru
え e   け ke   せ se   て te   ね ne   へ he   め me         れ re  ゑ(e)
お o   こ ko   そ so   と to   の no   ほ ho   も mo  よ yo  ろ ro  を o 
		 
       が ga   ざ za   だ da           ば ba   ぱ pa 
       ぎ gi   じ zi   ぢ(zi)          び bi   ぴ pi 
       ぐ gu   ず zu   づ(zu)          ぶ bu   ぷ pu 
       げ ge   ぜ ze   で de           べ be   ぺ pe 
       ご go   ぞ zo   ど do           ぼ bo   ぽ po 
                    
      きゃkya しゃsya ちゃtya にゃnya ひゃhya みゃmya         りゃrya 
      きゅkyu しゅsyu ちゅtyu にゅnyu ひゅhyu みゅmyu         りゅryu 
      きょkyo しょsyo ちょtyo にょnyo ひょhyo みょmyo         りょryo 
                                   
      ぎゃgya じゃzya                  びゃbya ぴゃpya 
      ぎゅgyu じゅzyu                  びゅbyu ぴゅpyu 
      ぎょgyo じょzyo                  びょbyo ぴょpyo
Characters in bold differ from those in Hepburn.
Characters in (parentheses) are obsolete.

Note that the "new" kana discussed above are not included, as they are not covered by any of the official standards.

The other rules of Kunrei match those of Hepburn with the following minor exceptions:

  • The indicator of a long vowel is the circumflex (ô), not the macron (ō).
  • Capital letters may be doubled instead of using the circumflex.
  • Syllabic n is always written as such, even the cases "np", "nb", "nm". (This matches modified Hepburn, but not the original.)
References

sci.lang.japan AFAQ 5.3.2
www.library.ucla.edu/libraries/eastasian/jpntable.htm
http://xembho.tripod.com/siryo/cabinet_order.html
http://xembho.tripod.com/iso3602/iso3602_unicode.html (Japanese)