Article I, Section 10, Clause 1 through 3. Article IV, Section 3, Clause 1. Basically Article IV says that no state may be admitted without the consent of the other states as expressed by a vote in Congress. Once allowed to join, states cannot split, combine, or change their border by a fraction of an inch without the consent of the other states as expressed through a vote in Congress. Article I, Section 10 lists a whole list of actions that could impact the interests and well being of the other states and which are forbidden entirely or allowed only with the consent of the other states as expressed though a vote in Congress. If states can join only with permission and once in can alter their borders only with permission and forbidden from a whole host of actions without permission then it isn't a stretch to conclude that permission is needed to leave as well.
Article I Section 10.
No State shall enter into any Treaty, Alliance, or Confederation; grant Letters of Marque and Reprisal; coin Money; emit Bills of Credit; make any Thing but gold and silver Coin a Tender in Payment of Debts; pass any Bill of Attainder, ex post facto Law, or Law impairing the Obligation of Contracts, or grant any Title of Nobility.
No State shall, without the Consent of the Congress, lay any Imposts or Duties on Imports or Exports, except what may be absolutely necessary for executing its inspection Laws: and the net Produce of all Duties and Imposts, laid by any State on Imports or Exports, shall be for the Use of the Treasury of the United States; and all such Laws shall be subject to the Revision and Controul of the Congress.
No State shall, without the Consent of Congress, lay any Duty of Tonnage, keep Troops, or Ships of War in time of Peace, enter into any Agreement or Compact with another State, or with a foreign Power, or engage in War, unless actually invaded, or in such imminent Danger as will not admit of delay.
Sure looks like a listing of things that states are prohibited from doing all right but I STILL can't discern a single word or phrase about secession.
Article IV Section 3.
New States may be admitted by the Congress into this Union; but no new State shall be formed or erected within the Jurisdiction of any other State; nor any State be formed by the Junction of two or more States, or Parts of States, without the Consent of the Legislatures of the States concerned as well as of the Congress.
The Congress shall have Power to dispose of and make all needful Rules and Regulations respecting the Territory or other Property belonging to the United States; and nothing in this Constitution shall be so construed as to Prejudice any Claims of the United States, or of any particular State.
I'm afraid I still can't see a thing about secession there! (Do I need some special glasses or something so I can see what is written between the lines in invisible ink?)
I will note that what IS plainly written there was completely overlooked by your pal Lincoln and his sock puppet congress when the state of West Virginia was formed.