Contrary to popular belief, no grammar rule prohibits starting a sentence with "however." As long as the usage fits the context and follows punctuation conventions, this and other transitional words, also known as adverbial conjunctions or conjunctive adverbs, may appropriately connect ideas and clarify the relationship between them. Contrast words like "however" can be used to indicate a contradiction.
Transitional words such as "however" require a comma after them when they indicate a contrast. Placement of the comma makes the reader pause, emphasizing the fact that a contrast comes next. For example:
"We all went home. However, she called a few minutes later."
Proper usage and punctuation clarifies that she remained in contact even though the parties had separated. "However" may also mean "in what manner" and thus comes at the beginning or in the middle of a sentence, as: "Fill in the blanks however you like" or "However you decide, the results will be the same." This difference in meaning and purpose accounts for the difference in punctuation.
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